Financial Markets

• Laurent Calvet [email protected] • John Lewis [email protected]

Topic 4:

HEC – MBA Financial Markets

The Internal Rate of Return

4-1

IRR Definition • IRR = The discounting rate that makes the Net Present Value (NPV) equal to zero • IRR is also called the Yield to Maturity • YTM used for securities • IRR used for capital expenditures, Venture Capital and Private Equity.

HEC – MBA Financial Markets

4-2

IRR • IRR is calculated using the same formula as the NPV except that the rate r is unknown: N

Fn =V 0 ∑ n n =1 (1 + r ) Where V0 is the initial investment in the project • The IRR is the rate r where the market value is equal to the present value of the future cash flows from the investment.

HEC – MBA Financial Markets

4-3

Computing IRR • The solution to the IRR formula is found through trial and error • Use a calculator or spreadsheet • Timing of cash flows is very important to calculation • Accurate models very carefully model the cash flows • Implementation shortfall arrives in an optimistic model of cash flows and the reality of actual magnitude and timing

HEC – MBA Financial Markets

4-4

IRR as an Investment Rule • Many companies have a target return on investment – either through policy or historical results. • In the NPV example, a project was started if the NPV was positive. • In the IRR case, the project is not started unless the return (r) of the project is above a certain threshold. HEC – MBA Financial Markets

4-5

Limitations of IRR and NPV • NPV and IRR can give opposing views of a project • Competition among investors and mechanisms of arbitrage theory move NVP towards zero • Therefore exceptional rates of return move towards the required rate of return • Can another investment with IRR = 15.89 be found to replace investment A in year 4? Year Investment A Investment B

Market Value Investment 10 -10 12.25 -12.25

Required Rate

HEC – MBA Financial Markets

1 9 5

2 3 5

3 0.5 0

4

5

6

7

0

2.1

0

5.1

NPV IRR $1.29 15.89% $2.32 11.05%

0.05

4-6

Which Investment A or B Year Investment A Investment B

Market Value Investment 10 -10 12.25 -12.25

Required Rate

1 9 5

2 3 5

3 0.5 0

4

5

6

7

0

2.1

0

5.1

NPV IRR $1.29 15.89% $2.32 11.05%

0.05

• Investment A has the lower NPV and higher IRR Capital is returned at the end of 3 years Years 4+ most likely to be reinvested at Required Rate of 5%

• IRR assumes that the return in year 4+ will be the same as from years 1 to 3. Will it?

HEC – MBA Financial Markets

4-7

Modified IRR - MIRR • Assumes cash flows are reinvested at the required rate of return • Calculate the terminal value of project by compounding all cash flows at required rate • Find the IRR with initial cash outlay at beginning of the project and the terminal value of project Year Investment A Investment B

Market Value Investment 10 -10 12.25 -12.25

Discount Rate Investment A Investment B

HEC – MBA Financial Markets

1 9 5

2 3 5

3 0.5 0

4

5

6

7

0

2.1

0

5.1

NPV IRR $1.29 15.89% $2.32 11.05%

0 16.5 0 20.5

M-NPV MIRR 16.4975 7.41% 20.4971 7.63%

0.05 -10 -12.25

0 0

0 0

0 0

0 0

0 0

4-8

Modified IRR • Reconciles NPV and IRR models • Realistic view that follow-on investments will not have abnormally high returns • The value computed by MIRR matches real outcomes • If the IRR returns are not possible to replicate – might it be better to return the cash flows to the shareholders? Question for Corporate Finance Class.

HEC – MBA Financial Markets

4-9

Special Cases for IRR • No IRR - NPV remains positive for all discount rates. • Multiple IRRs Due to initial cash inflows and later high costs Unsure which IRR is the correct IRR

• Investments that may have initial inward cash flows before expenses must be paid. This is effectively a loan Subscriptions before materials are produced

• IRR does not have a time varying rate of return • You know you have one of these when Excel returns #NUM

HEC – MBA Financial Markets

4 - 10

Mutually Exclusive Projects • Must select from a list of promising projects • Cannot select Project A and B – they are mutually exclusive • Inability to select both is often from Capital Rationing Hard rationing – cannot obtain funds at market rate • Market imperfections, transaction costs, agency costs…

Soft Rationing – Internally imposed financial constraints • Limits on borrowing and unable to raise equity cash • Steady growth strategy • Annual capital limits within divisions

HEC – MBA Financial Markets

4 - 11

Mutually Excl. - Scale • Another form of the NPV and IRR disagreement problem. • A large scale project has a high NPV and lower IRR while a small scale project has a low NPV with a higher IRR. • The large scale, high NPV, project creates more wealth for shareholders • From a straight IRR view, the small scale project is a better use of funds.

HEC – MBA Financial Markets

4 - 12

Incremental IRR • To select between a large scale high NPV and a small scale high IRR project, create an incremental project that has the cash flows equal to the difference of the cash flows for the two projects. • Decision rule: If incremental IRR is higher than the required rate then select the large scale project. If incremental IRR is lower than required rate then select small scale project. • The incremental project is a combination of the two projects. Both projects have a positive NPV and IRR above the threshold. If we accept the large scale project it is the same as accepting the cash flows from the incremental project and the small scale project. The decision rule is on the incremental project. HEC – MBA Financial Markets

4 - 13

Incremental IRR - example • Required rate = 10%, IRR threshold = 15% • Order of creating incremental project is important subtract cash flow so initial investment remains negative Apply decision rule – select larger project if incremental IRR is above the threshold (or use NPV Rule)

Project Small scale Large scale Incremental

HEC – MBA Financial Markets

F0

F1 -10 -100 -90

IRR NPV(10%) 15.00 50% $3.64 120.00 20% $9.09 105.00

17%

$5.45

4 - 14

Timing Problem • Projects with the same initial outflows but different inflow characteristics. • In straight IRR terms, the project with near term inflows will have a better IRR than a project with later, and larger, inflows • Must use the NPV to decide between projects. Decision depends on the discount rate. • Reliance on just IRR leads to ‘short-term’ optimal results. A problem in public companies that are very conscious of quarterly numbers. HEC – MBA Financial Markets

4 - 15

Timing Problem - example • Two projects with identical outflows and different inflows. • Decision between projects depends on discount rate used to calculate NPV. Notice change in NPV at different discount rate Which project would you choose and why? At high discount rate – money is more valuable today

Project A Project B

HEC – MBA Financial Markets

0 -10000 -10000

1 8000 0

2 3 IRR NPV (5%) 3000 1000 14% $1,203.97 2000 11500 11% $1,748.19

NPV(12%) $503.38 $293.01

4 - 16

• Laurent Calvet [email protected] • John Lewis [email protected]

Topic 4:

HEC – MBA Financial Markets

The Internal Rate of Return

4-1

IRR Definition • IRR = The discounting rate that makes the Net Present Value (NPV) equal to zero • IRR is also called the Yield to Maturity • YTM used for securities • IRR used for capital expenditures, Venture Capital and Private Equity.

HEC – MBA Financial Markets

4-2

IRR • IRR is calculated using the same formula as the NPV except that the rate r is unknown: N

Fn =V 0 ∑ n n =1 (1 + r ) Where V0 is the initial investment in the project • The IRR is the rate r where the market value is equal to the present value of the future cash flows from the investment.

HEC – MBA Financial Markets

4-3

Computing IRR • The solution to the IRR formula is found through trial and error • Use a calculator or spreadsheet • Timing of cash flows is very important to calculation • Accurate models very carefully model the cash flows • Implementation shortfall arrives in an optimistic model of cash flows and the reality of actual magnitude and timing

HEC – MBA Financial Markets

4-4

IRR as an Investment Rule • Many companies have a target return on investment – either through policy or historical results. • In the NPV example, a project was started if the NPV was positive. • In the IRR case, the project is not started unless the return (r) of the project is above a certain threshold. HEC – MBA Financial Markets

4-5

Limitations of IRR and NPV • NPV and IRR can give opposing views of a project • Competition among investors and mechanisms of arbitrage theory move NVP towards zero • Therefore exceptional rates of return move towards the required rate of return • Can another investment with IRR = 15.89 be found to replace investment A in year 4? Year Investment A Investment B

Market Value Investment 10 -10 12.25 -12.25

Required Rate

HEC – MBA Financial Markets

1 9 5

2 3 5

3 0.5 0

4

5

6

7

0

2.1

0

5.1

NPV IRR $1.29 15.89% $2.32 11.05%

0.05

4-6

Which Investment A or B Year Investment A Investment B

Market Value Investment 10 -10 12.25 -12.25

Required Rate

1 9 5

2 3 5

3 0.5 0

4

5

6

7

0

2.1

0

5.1

NPV IRR $1.29 15.89% $2.32 11.05%

0.05

• Investment A has the lower NPV and higher IRR Capital is returned at the end of 3 years Years 4+ most likely to be reinvested at Required Rate of 5%

• IRR assumes that the return in year 4+ will be the same as from years 1 to 3. Will it?

HEC – MBA Financial Markets

4-7

Modified IRR - MIRR • Assumes cash flows are reinvested at the required rate of return • Calculate the terminal value of project by compounding all cash flows at required rate • Find the IRR with initial cash outlay at beginning of the project and the terminal value of project Year Investment A Investment B

Market Value Investment 10 -10 12.25 -12.25

Discount Rate Investment A Investment B

HEC – MBA Financial Markets

1 9 5

2 3 5

3 0.5 0

4

5

6

7

0

2.1

0

5.1

NPV IRR $1.29 15.89% $2.32 11.05%

0 16.5 0 20.5

M-NPV MIRR 16.4975 7.41% 20.4971 7.63%

0.05 -10 -12.25

0 0

0 0

0 0

0 0

0 0

4-8

Modified IRR • Reconciles NPV and IRR models • Realistic view that follow-on investments will not have abnormally high returns • The value computed by MIRR matches real outcomes • If the IRR returns are not possible to replicate – might it be better to return the cash flows to the shareholders? Question for Corporate Finance Class.

HEC – MBA Financial Markets

4-9

Special Cases for IRR • No IRR - NPV remains positive for all discount rates. • Multiple IRRs Due to initial cash inflows and later high costs Unsure which IRR is the correct IRR

• Investments that may have initial inward cash flows before expenses must be paid. This is effectively a loan Subscriptions before materials are produced

• IRR does not have a time varying rate of return • You know you have one of these when Excel returns #NUM

HEC – MBA Financial Markets

4 - 10

Mutually Exclusive Projects • Must select from a list of promising projects • Cannot select Project A and B – they are mutually exclusive • Inability to select both is often from Capital Rationing Hard rationing – cannot obtain funds at market rate • Market imperfections, transaction costs, agency costs…

Soft Rationing – Internally imposed financial constraints • Limits on borrowing and unable to raise equity cash • Steady growth strategy • Annual capital limits within divisions

HEC – MBA Financial Markets

4 - 11

Mutually Excl. - Scale • Another form of the NPV and IRR disagreement problem. • A large scale project has a high NPV and lower IRR while a small scale project has a low NPV with a higher IRR. • The large scale, high NPV, project creates more wealth for shareholders • From a straight IRR view, the small scale project is a better use of funds.

HEC – MBA Financial Markets

4 - 12

Incremental IRR • To select between a large scale high NPV and a small scale high IRR project, create an incremental project that has the cash flows equal to the difference of the cash flows for the two projects. • Decision rule: If incremental IRR is higher than the required rate then select the large scale project. If incremental IRR is lower than required rate then select small scale project. • The incremental project is a combination of the two projects. Both projects have a positive NPV and IRR above the threshold. If we accept the large scale project it is the same as accepting the cash flows from the incremental project and the small scale project. The decision rule is on the incremental project. HEC – MBA Financial Markets

4 - 13

Incremental IRR - example • Required rate = 10%, IRR threshold = 15% • Order of creating incremental project is important subtract cash flow so initial investment remains negative Apply decision rule – select larger project if incremental IRR is above the threshold (or use NPV Rule)

Project Small scale Large scale Incremental

HEC – MBA Financial Markets

F0

F1 -10 -100 -90

IRR NPV(10%) 15.00 50% $3.64 120.00 20% $9.09 105.00

17%

$5.45

4 - 14

Timing Problem • Projects with the same initial outflows but different inflow characteristics. • In straight IRR terms, the project with near term inflows will have a better IRR than a project with later, and larger, inflows • Must use the NPV to decide between projects. Decision depends on the discount rate. • Reliance on just IRR leads to ‘short-term’ optimal results. A problem in public companies that are very conscious of quarterly numbers. HEC – MBA Financial Markets

4 - 15

Timing Problem - example • Two projects with identical outflows and different inflows. • Decision between projects depends on discount rate used to calculate NPV. Notice change in NPV at different discount rate Which project would you choose and why? At high discount rate – money is more valuable today

Project A Project B

HEC – MBA Financial Markets

0 -10000 -10000

1 8000 0

2 3 IRR NPV (5%) 3000 1000 14% $1,203.97 2000 11500 11% $1,748.19

NPV(12%) $503.38 $293.01

4 - 16