Homework Sourse1 Project P costs 15000 and is expected to produce benefits
1. Project P costs $15,000 and is expected to produce benefits (cash flows) of $4,500 per year for five years. Project Q costs $37,500 and is expected to produce cash flows of $11,100 per year for five years. Calculate each project’s (a) net present value (NPV), (b) internal rate of return (IRR), and (c) mod- ified internal rate of return (MIRR). The firm’s required rate of return is 14 percent.
2. Compute the (a) NPV, (b) IRR, (c) MIRR, and (d) discounted payback for the following independent capital budgeting projects. (r = 9%)
Which project(s) should the company purchase? Why?
Solution
Project P Costs $15,000 Benefits 4500 Project Q Costs 37500 Benefits 11100 Net Present Value Project P Year Cash flow Discount factor @ 14% Present value 0 -15000 1 -15000 1 4500 0.877192982 3,947.37 2 4500 0.769467528 3,462.60 3 4500 0.674971516 3,037.37 4 4500 0.592080277 2,664.36 5 4500 0.519368664 2,337.16 NPV 448.86 Project Q Year Cash flow Discount factor @ 14% Present value 0 -37500 1 -37500 1 11100 0.877192982 9,736.84 2 11100 0.769467528 8,541.09 3 11100 0.674971516 7,492.18 4 11100 0.592080277 6,572.09 5 11100 0.519368664 5,764.99 NPV 607.20 The IRR of the project would be, using the IRR function in excel we get Project P Year Cash flow Discount factor @ 15.24% Present value 0 -15000 1.00000 -15000 1 4500 0.86775 3,904.89 2 4500 0.75300 3,388.49 3 4500 0.65342 2,940.38 4 4500 0.56701 2,551.52 5 4500 0.49202 2,214.10 NPV (0.62) IRR(I40:I45,15%) 15.23823712% Project Q Year Cash flow Discount factor @ 14.672% 0 -37500 1.00000 -37500 1 11100 0.87205 9679.782336 2 11100 0.76048 8441.278024 3 11100 0.66317 7361.237289 4 11100 0.57832 6419.385106 5 11100 0.50433 5598.040591 -0.276654364 IRR of project Q is approx 14.672% Project P FV of cash flow with cost of capital @ 14% 8,664.37 7,600.32 6,666.95 5,848.20 5,130.00 33,909.83 MIRR = ((33909.83)/15000)^1/5 -1 17.72% Project Q FV of cash flow with cost of capital @ 14% 21,372.10 18,747.46 16,445.14 14,425.56 12,654.00 83,644.26 MIRR = ((83644.26)/37500)^1/5 -1 17.40% Net Present Value Project P Year Cash flow Discount factor @ 9% Present value 0 -15000 1 -15000 1 4500 0.917431193 4,128.44 2 4500 0.841679993 3,787.56 3 4500 0.77218348 3,474.83 4 4500 0.708425211 3,187.91 5 4500 0.649931386 2,924.69 NPV 2,503.43 Project Q Year Cash flow Discount factor @ 9% Present value 0 -37500 1 -37500 1 11100 0.917431193 10,183.49 2 11100 0.841679993 9,342.65 3 11100 0.77218348 8,571.24 4 11100 0.708425211 7,863.52 5 11100 0.649931386 7,214.24 NPV 5,675.13 As per the NPV method Project Q should be selected as it has higher NPV The IRR of both the project would be the same as calculated earlier Project P 15.24% Project Q 14.67% As per IRR Project P should be selected as it has higher IRR Project P FV of cash flow with cost of capital @ 9% 6,923.81 6,352.12 5,827.63 5,346.45 4,905.00 29,355.01 MIRR = ((29355.01)/15000)^1/5 -1 14.37% Project Q FV of cash flow with cost of capital @ 9% 17,078.73 15,668.56 14,374.82 13,187.91 12,099.00 72,409.01 MIRR = ((72409.01)/37500)^1/5 -1 14.06% As per MIRR project P should be selected since it has higher MIRR Discounted Payback Project P Year -15000 1 -15000 -15000 4500 0.917431193 4128.440367 -10871.6 4500 0.841679993 3787.55997 -7084 4500 0.77218348 3474.82566 -3609.17 4500 0.708425211 3187.91345 -421.261 4500 0.649931386 2924.691238 2503.431 The payback period is 4 yrs and (-421.261/2924.691238) Discounted payback is 4.14 yrs Discounted Payback Project Q Year -37500 1 -37500 -37500 11100 0.917431193 10183.48624 -27316.5 11100 0.841679993 9342.647925 -17973.9 11100 0.77218348 8571.236629 -9402.63 11100 0.708425211 7863.519843 -1539.11 11100 0.649931386 7214.238388 5675.129 The payback period is 4 yrs and (-1539.11/7214.238388) Discounted payback is 4.21 yrs As per discounted payback project P should be selected since it has lower payback period
