Question

You are evaluating the following project. All $ are in millions Initial cost of the project at t=0 is $70. Annual cash flows from the project depends on the demand for the product and is estimated to be as follows: With probability of 30%, the demand is high and the annual cash flow is $45 With probability of 40%, the demand is average and the annual cash flow is $30 With probability of 30%, the demand is low and the annual cash flow is $15 The above cash flows occur for the next 3 years, that is, until from t=1 to t=3. The company plans to finance the project by issuing bonds and stocks. The company will issue a ten-year bond at par with the coupon rate of 5%. The company’s stock has a beta of 2.1. The risk-free rate is 2.07% and the market risk premium is 6%. The marginal tax rate of the firm is 40%. The firm’s target and current capital structure is 40% debt and 60% equity. Questions: (In your calculations, please keep up to two decimal points after %. For example, 12.34%.) 1. What is the expected NPV of the project? 2. What feature of the project makes the managers hesitant with starting this project? 3. Now assume that if we wait one year, we will gain additional information regarding demand. That is, at t=1, we will know whether the demand will be high, average, or low. (The probability of the demand is 30%,40%,30% at t=0 and then becomes certain at t=1). Find out the expected NPV of the project. 3. Now assume that if we wait one year, we will gain additional information regarding demand and can decide whether to do the project or not at t=1. That is, at t=1, we will know whether the demand for the product will be high, average, or low. (The probability of the demand is 30%,40%,30% at t=0 and then becomes certain at t=1). If you decide to do the project at t=1, the initial cost occurs at t=1, and cash flow according to the demand type will stay the same during the life of the project until t=4. Find out the expected NPV of the project at t=0.

Answer 1

All cash flows are in $ mn

Initial investment, C₀ = 70

N = number of years = 3

Cost of debt, Kd = YTM = Coupon rate (as bond is issued at par) = 5%

Cost of equity, Ke = risk free rate + Beta x market premium = 2.07% + 2.1 x 6% = 14.67%

Proportion of debt = Wd = 40%

Proportion of equity, We = 60%

Tax rate, T = 40%

Hence, Discount rate = R = WACC = Wd x Kd x (1 - T) + We x Ke = 40% x 5% x (1 - 40%) + 60% x 14.67% = 10.00%

Part (1)

Probability of high demand = P_high = 30%; Expected annual cash flows, C_high = 45

Hence, NPV_high = - C₀ + C_high / R x [1 - (1 + R)^-N] = - 70 + 45 / 10% x [1 - (1 + 10%)^-3] = $ 41.90

Probability of average demand = P_average = 40%; Expected annual cash flows, C_average = 30

Hence, NPV_average = - C₀ + C_average / R x [1 - (1 + R)^-N] = - 70 + 30 / 10% x [1 - (1 + 10%)^-3] = $ 4.60

Probability of low demand = P_low = 30%; Expected annual cash flows, C_low = 15

Hence, NPV_low = - C₀ + C_low / R x [1 - (1 + R)^-N] = - 70 + 15 / 10% x [1 - (1 + 10%)^-3] = - $ 32.70

Hence, expected NPV = P_high x NPV_high + P_average x NPV_average​​​​ + P_low x NPV_low​​​ = 30% x 41.90 + 40% x 4.06 + 30% x (- 32.70) = 4.60

Part (2)

Features leading to hesitation:

• Very high risk of the project evident in high beta
• 30% probability of low demand leading to a low annual cash inflows

Part (3)

After waiting for 1 year, the demand will be certain and the firm will undertake the project only if it has positive NPV. That means the firm will undertake the project only if demand is high or average. It will not undertake the project if demand is low.

Hence, expected NPV after one year i.e. at t= 1 will be = P_high x NPV_high + P_average x NPV_average​​​​ = 30% x 41.90 + 40% x 4.60 = 14.41

Hence, NPV today = NPV after 1 year / (1 + R) = 14.41 / (1 + 10%) = 13.10