Question

Jojo's Bizzare is taking on two projects. The cost of project A is $ 70,000 and the cost of B is $ 140,000. The firm’s cost of capital is 12% per year. After-tax cash flows are estimated to be $ 10,000 per year forever for project A. After-tax cash flow at time 1 will be $12,000 for the project B. However, the future cash flows from Project B are expected to increase by 3% per year forever. Compute NPV and IRR for both projects. Which project should Jojo's undertake? At what growth rate of future cash flows for the project B would Jojo's be indifferent? (NPVA = NPVB )? The cost of capital for both projects is still 12% per year.

Answer 1

Computation of NPV and IRR for Project A:

NPV = PV of future cash flow – Initial investment

      = Annual cash flow/Rate of return – Initial investment

NPVA = ($ 10,000/0.12) - $ 70,000

       = $ 83,333.33333 - $ 70,000

        = $ 13,333.33333 or $ 13,333.33

NPV at a discount rate equals to IRR is zero.

0 = $ 10,000/IRR – $ 70,000

$ 70,000 = $ 10,000/IRR

IRR = $ 10,000/$ 70,000 = 0.142857143 or 14.29 %

NPV of Project A is $ 13,333.33 and IRR is 14.29 %

Computation of NPV and IRR for Project B:

NPV = PV of future cash flow – Initial investment

      = [Annual cash flow/ (Rate of return- growth rate)] – Initial investment

NPVB = $ 12,000/ (0.12-0.03) - $ 140,000

       = ($ 12,000/ 0.09) - $ 140,000

        = $ 133,333.3333 - $ 140,000

       = - $ 6,666.666667 or - $ 6,666.66

NPV at a discount rate equals to IRR is zero.

0 = $ 12,000/(IRR-0.03) – $ 140,000

$ 140,000 = $ 12,000/(IRR-0.03)

IRR – 0.03 = $ 12,000/$ 140,000 = 0.085714286

IRR = 0.085714286 + 0.03 = 0.115714286 or 11.57 %

NPV of Project B is - $ 6,666.66 and IRR is 11.57 %

Jojo should undertake Project A as it has positive NPV and IRR higher than required rate of return.

NPV A = NPV B

NPVB = $ 13,333.33

$ 13,333.33 = $ 12,000/ (0.12 - g) - $ 140,000

$ 12,000/ (0.12 - g) = $ 140,000 + $ 13,333.33

                                = $ 153,333.33

0.12 – g = $ 12,000/$ 153,333.33

             = 0.07826087126654

g = 0.12 - 0.07826087126654 = 0.04173912873346 or 4.1739 %

A growth rate of 4.1739 % for future cash flow for Project B will Jojo’s be indifferent.