Question

Star Wars & Company is considering the replacement of its old, fully depreciated blasters. Two new models are available: Type 168-3, which has a cost of $265,000, a 4-year expected life, and after-tax cash flows (labor savings and depreciation) of $96,500 per year; and Type 190-6, which has a cost of 465,000, a 8-year life, and after-tax cash flows of $101,800 per year. Blaster prices are not expected to rise, because inflation will be offset by cheaper components (microprocessors) used in the modern blasters.

1. Assume that Star Wars' cost of capital is 12%. Calculate the two Blaster Types' NPVs. Round your answers to the nearest cent. (Hint: Adjust the NPV for the Blaster Type with the shorter length)
2. Should the firm replace its old Blaster, and, if so, which new Blaster Type should it use?
3. By how much would the value of the company increase if it accepted the better Blaster Type? Round your answer to the nearest cent. (hint:pick the higher valued Blaster from Part a).
4. What is the equivalent annual annuity for each Blaster Type? Round your answer to the nearest cent.

Answer 1

Part (a)

Cost of capital, r = 12%

Type 168-3, which has a cost of $265,000, a 4-year expected life, and after-tax cash flows (labor savings and depreciation) of $96,500 per year;

Hence, NPV = - Initial investment + PV of annual cashflows as annuity = - 265,000 + 96,500 / 12% x [1 - (1 + 12%)^-4] = $  28,104.21

In order to match the term of 8 years, we will have to repeat this investment at the end of year 4.

Hence, effective NPV of Type 168-3 will be =  28,104.21 +  28,104.21 / (1 + 12%)⁴ = $  45,964.95

Type 190-6, which has a cost of 465,000, a 8-year life, and after-tax cash flows of $101,800 per year.

NPV for Type 190-6 = - 465,000 + 101,800 / 12% x [1 - (1 + 12%)^-8] = $  40,705.73

Part (b)

NPV for both the machines are positive. Hence, the firm should replace the old blaster. It should choose Type 168-3 as it has higher NPV over the same term of 8 years.

Part (c)

Increase in the value of the company increase if it accepted the better Blaster Type = NPV of Type 168-3 = $ 45,964.95 (considering the matching term of 8 years for this machine)

Part (d)

Equivalent annual annuity = NPV x r / [1 - (1 + r)^-n]

Hence, Equivalent annual annuity for Type 168-3 = 45,964.95 x 12% / [1 - (1 + 12%)^-8] = $  9,252.87

and Equivalent annual annuity for Type 190-6 = 40,705.73 x 12% / [1 - (1 + 12%)^-8] = $   8,194.18