Question

1. Consider two projects with the following (after-tax) cash flows. Project A: CF1 50, CF2 55, CF3 85. Project B: CF1 140. Both projects require an initial investment of 100. Assume the cost of capital for both projects is r 5%.

(a) Compute NPV and IRR for project A.

(b) Compute NPV and IRR for project B.

(c) Assume you replicate project B twice, i.e. reinvest 100 in t 1 and t2. Compute the NPV and IRR of the replicated project.

(d) Consider again the 1-year project B. Compute the (annualized) modified IRR assuming a reinvestment rate of 10%.

(e) Convert project A and project B into equivalent annuities (see slide 47).

2. Consider a two-year project with a 50% chance of success and failure. If successful, the project generates 100 per year, if not it generates 20 per year. The project requires an initial investment of 50 and the discount rate is 10%.

(a) What is the expected NPV?

(b) What is the probability that NPV < 0?

(c) Assume you can terminate the project after one year, i.e. after the first cash flow is realized. If you choose to terminate, you are able to recoup 50 (paid at the end of t 1).

i. What is the expected NPV?

ii. What is the probability that NPV < 0?

iii. What is the value of the option to terminate?

Answer 1

Ans.(a). Net Present Value(NPV) and Internal Rate of Return(IRR) of Project A:

NPV = Present value of Cash inflows - Present value of cash outflows

Cashflow in year 1 (1+r)1 Cashflow in year n NPV = Cashflow in year 2 Cashflow in year 3 (1+r)2 + (1 + r) 3 + ... + (1 + r) -Initial Outlay

Here, r is the cost of capital

NPV = $150 $55 $85 |(1 + 5%)1+ (1 + 5%)2 + (1 + 5%)*|- $100

NPV = $166

Internal Rate of Return(IRR) is the return that the project will give if the NPV of the project is zero.

$150 $55 $85 NPV = ((1+r)1+ (1+r)2+(1+r)30 - $

$85 $150 = |a1 + IRR) 1 $55 (1 +IRR)2*(1 +IRR)

On solving, we get IRR of Project A= 99%

Ans. b. NPV and IRR of Project B:

Project B is only a one year project and generates $140 in year 1.

NPV = $140 (1 + 5%) (1 + 50 - $100

= $33

IRR of Project B:

IRR is calculated by keeping the NPV equal to zero.

NPV = 0 = $140 |(1+IRR)

Therefore, IRR of project B is 40%.

Ans. c.

On replicating the project B in the first and second year, we get a new set of cashflows. We can calculate the NPV as in image below:

Replicated Project B: Year -100 Cashflow Reinvestment Final Cashflow Present Value -$100 -$100 $140 -$100 $40 $38.10 $140 -$100 $40 $36.28 $140 $140 $120.94 $40 (1 + 5%) 2 3 NPV = -$100 + $38.10 + $36.28 + $120.94 NPV: $95

IRR of replicated project B is:

$40 $40 $140 1 NPV = V = (1+r)1+ (1+r)2+(1+r)31 - $11

$40 0 = $40 $140 |(1 + IRR)1 + (1 + IRR)2 + (1+1RR)*|-

therefore, IRR = 40%. Therefore, the replicated project gives the same internal rate of return as the previous project B.