By NEAS - 2/16/2021 10:44:15 PM
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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