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

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NEAS	NEAS posted 3 Years Ago #16570 #
Supreme Being Group: Administrators Posts: 4.5K, Visits: 1.6K	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 0
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