Corporate finance, Module 4: IRR and NPV sample final exam problem


Corporate finance, Module 4: IRR and NPV sample final exam problem

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Corporate finance, Module 4: IRR and NPV sample final exam problem

Exercise 4.1: IRR vs NPV

A firm has three projects (S = short; M = medium; L = long), each with an opportunity cost of capital of CC and one initial investment at time t=0. The initial investment differs for the three projects.

●    Project S has one cash inflow of S1 at time t=1.
●    Project M has cash inflows of M1 and M2 at times t=1 and t=2.
●    Project L has cash inflows of L1, L2, and L3 at times t=1, t=2, and t=3.

❏    Projects S and M have the same IRR.
❏    Projects S and L have the same NPV.

The IRR of Project L is R%.

A.    What is the initial investment (at time t=0) of project L?
B.    What is the NPV of Project L?
C.    What is the initial investment (at time t=0) of project S?
D.    What is the IRR of Project S?
E.    What is the initial investment (at time t=0) of project M?
F.    What is the NPV of Project M?

Part A: Project L has an IRR of R, so its initial investment =

    L1 / (1+R)1 + L2 / (1+R)2 + L3 / (1+R)3 = Linvest

Part B: With an opportunity cost of capital of CC, the NPV for Project L is

    -Linvest + L1 / (1+CC)1 + L2 / (1+CC)2 + L3 / (1+CC)3 = Lnpv

Part C: Project S has the same NPV as Project L, so its NPV is also Lnpv. Its initial investment is

Lnpv = – Sinvest + S1 / (1+CC)1 ➾

Sinvest = -Lnpv + S1 / (1+CC)1

Part D: We compute the IRR of Project S:

Sinvest = S1 / (1+Sirr)1 ➾ Sirr = S1 / Sinvest – 1
Part E: Project M has the same IRR as Project S, or Sirr. Its initial investment is

    M1 / (1+Sirr)1 + M2 / (1+Sirr)2 = Minvest

Part F: The NPV of Project M at an opportunity cost of capital of CC is

Lnpv = – Minvest + M1 / (1+CC)1 + M2 / (1+CC)2


Exercise 4.2: IRR vs NPV

A firm has three projects (S = short; M = medium; L = long), each with an opportunity cost of capital of CC and one initial investment at time t=0. The initial investment differs for the three projects.

●    Project S has one cash inflow of 2,014.23 at time t=1.
●    Project M has cash inflows of 448.18 each at times t=1 and t=2.
●    Project L has cash inflows of 268.95 each at times t=1, t=2, and t=3.

❏    Projects S and M have the same IRR.
❏    Projects S and L have the same NPV.

The IRR of Project L is 16%.

A.    What is the initial investment (at time t=0) of project L?
B.    What is the NPV of Project L?
C.    What is the initial investment (at time t=0) of project S?
D.    What is the IRR of Project S?
E.    What is the initial investment (at time t=0) of project M?
F.    What is the NPV of Project M?

Part A: Project L has an IRR of R, so its initial investment =

    268.95 / (1+ 0.16)1 + 268.95 / (1+ 0.16)2 + 268.95 / (1+ 0.16)3 = 604.03

Part B: With an opportunity cost of capital of CC, the NPV for Project L is

    –604.03 + 268.95 / (1+ 0.13)1 + 268.95 / (1+ 0.13)2 + 268.95 / (1+ 0.13)3 = 31.00

Part C: Project S has the same NPV as Project L, so its NPV is also Lnpv. Its initial investment is

31.00 = – Sinvest + 2,014.23 / (1+ 0.13)1 ➾

Sinvest = –31.00 + 2,014.23 / (1+ 0.13)1 = 1,751.50

Part D: We compute the IRR of Project S:

1,751.50 = 2,014.23 / (1+Sirr)1 ➾ Sirr = 2,014.23 / 1,751.50 – 1 = 15.00%
Part E: Project M has the same IRR as Project S, or Sirr. Its initial investment is

    Minvest = 448.18 / (1+ 0.15)1 + 448.18 / (1+ 0.15)2 = 728.61

Part F: The NPV of Project M at an opportunity cost of capital of CC is

Lnpv = –728.61 + 448.18 / (1+ 0.13)1 + 448.18 / (1+ 0.13)2 = 19.00


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