Question

Hack Wellington Co. is considering a three-year project that will require an initial investment of $55,000. It has estimated that the annual cash flows for the project under good conditions will be $40,000 and $7,000 under bad conditions. The firm believes that there is a 60% chance of good conditions and a 40% chance of bad conditions.

1. If the firm is using a weighted average cost of capital of 13%, the expected net present value (NPV) of the project is

1. $4,553

2. $7,037

3. $5,381

4. $8,279

Hack Wellington Co. wants to take a potential growth option into account when calculating the project’s expected NPV. If conditions are good, the firm will be able to invest $4,000 in year 2 to generate an additional cash flow of $14,000 in year 3. If conditions are bad, the firm will not make any further investments in the project.

2. Using the information from the preceding problem, the expected NPV of this project—when taking the growth option into account—is

1. $14,665

2. $10,999

3. $12,832

4. $12,221

3. Hack Wellington Co.’s growth option is worth

1. $3,942

2. $3,548

3. $4,336

4. $3,745

Answer 1

1. If the firm is using a weighted average cost of capital of 13%, the expected net present value (NPV) of the project is $ 8,279

Calculation :

a. Calculation of Expected Cash flow :

It is given that It has estimated that the annual cash flows for the project under good conditions will be $40,000 and $7,000 under bad conditions. The firm believes that there is a 60% chance of good conditions and a 40% chance of bad conditions.

Therefore, Expected cash flow every year be : $ ( 40,000 x 60% ) + $ ( 7,000 x 40% ) = $ 24,000 + 2800 = $ 26800 per year

b. Expected net present value (NPV) of the project :

= Weigted average cash flow for life of project - Initial Investment

= (Cashflow for the period x discounting factor at 13% cost of capital for 3 years ) - Initial Investment

= ( $ 26,800 x ( 0.8849+0.7830+0.6930 )) - $ 55000

= $ 8279

2. Using the information from the preceding problem, the expected NPV of this project—when taking the growth option into account—is $ 12221

Calculation :

It is given that  If conditions are good, the firm will be able to invest $4,000 in year 2 to generate an additional cash flow of $14,000 in year 3. If conditions are bad, the firm will not make any further investments in the project.

By using same projection

Expected net present value (NPV) of the project :

= Weigted average cash flow for life of project - Initial Investment - Additional Investment at discounted price

= (Cashflow for the period xdiscounting factor at 13% c ost of capital for 3 years ) - Initial Investment - Additional Investmet x discounting factor at 13% c ost of capital at 3 year

= ( $ 26,800 x ( 0.8849+0.7830+0.6930 )) +( $ 14,000 x 60% x 0.8849) - $ 55000 - ( $ 4,000 )

= $ 12221

Here, it is noted that the cash flow is generated additionally in the next year of additional investment hence the additional cash flow is discounted as per discounted factor of 1st year end of investment means at the end of the year of investment. Therefore, the year 1 discounted factor is connsidered while calculating NPV.

3. Hack Wellington Co.’s growth option is worth be $ 3942

Calculation = $ 12221 - $ 8729 = $ 3942