In: Finance
Sigma Pty. Ltd. is evaluating whether to buy pieces of medical equipment each of which requires an up-front expenditure of $1.5 million. The projects are expected to produce the following net cash inflows:
Year Equipment A Equipment B
1 $500,000 $2,000,000
2 $1,000,000 $1,000,000
3 $2,000,000 $600,000
a. What is the internal rate of return for each piece of equipment?
b. What is the payback period for each machine?
c. What is the net present value of each machine if the cost of capital is 10 per cent? 5 per cent? 15 per cent?
d. Should Better Health buy both machines, only one, or none? Explain your answer
a)
Equipment A:
Internal rate of return is the rate that makes NPV equal to 0
NPV = -1,500,000 + 500,000 / (1 + R)1 + 1,000,000 / (1 + R)2 + 2,000,000 / (1 + R)3
Using trial and error method, i.e., after trying various values for R, lets try R as 43.97%
NPV = -1,500,000 + 500,000 / (1 + 0.4397)1 + 1,000,000 / (1 + 0.4397)2 + 2,000,000 / (1 + 0.4397)3
NPV = = 0
Therefore, IRR of equipment A is 43.97%
Equipment B:
Internal rate of return is the rate that makes NPV equal to 0
NPV = -1,500,000 + 2,000,000 / (1 + R)1 + 1,000,000 / (1 + R)2 + 600,000 / (1 + R)3
Using trial and error method, i.e., after trying various values for R, lets try R as 82.03%
NPV = -1,500,000 + 2,000,000 / (1 + 0.8203)1 + 1,000,000 / (1 + 0.8203)2 + 600,000 / (1 + 0.8203)3
NPV = = 0
Therefore, IRR of equipment B is 82.03%
b)
Equipment A:
Cumulative cash flow for year 0 = -1,500,000
Cumulative cash flow for year 1 = -1,500,000 + 500,000 = -1,000,000
Cumulative cash flow for year 2 = -1,000,000 + 1,000,000 = 0
Payback period of equipment A is 2 years
Equipment B:
Cumulative cash flow for year 0 = -1,500,000
Cumulative cash flow for year 1 = -1,500,000 + 2,000,000 = 500,000
Payback period of equipment B is 1 year
c)
Equipment A:
net present value = Present value of cash inflows - present value of cash outflows
Net present value = -1,500,000 + 500,000 / (1 + 0.1)1 + 1,000,000 / (1 + 0.1)2 + 2,000,000 / (1 + 0.1)3
Net present value = $1,283,621.34
Net present value = -1,500,000 + 500,000 / (1 + 0.05)1 + 1,000,000 / (1 + 0.05)2 + 2,000,000 / (1 + 0.05)3
Net present value = $1,610,895.15
Net present value = -1,500,000 + 500,000 / (1 + 0.15)1 + 1,000,000 / (1 + 0.15)2 + 2,000,000 / (1 + 0.15)3
Net present value = $1,005,958.74
Equipment B:
net present value = Present value of cash inflows - present value of cash outflows
Net present value = -1,500,000 + 2,000,000 / (1 + 0.1)1 + 1,000,000 / (1 + 0.1)2 + 600,000 / (1 + 0.1)3
Net present value = $1,595,416.98
Net present value = -1,500,000 + 2,000,000 / (1 + 0.05)1 + 1,000,000 / (1 + 0.05)2 + 600,000 / (1 + 0.05)3
Net present value = $1,830,093.94
Net present value = -1,500,000 + 2,000,000 / (1 + 0.15)1 + 1,000,000 / (1 + 0.15)2 + 600,000 / (1 + 0.15)3
Net present value = $1,389,783.84
d)
Health should buy both machines as it has IRRs greater than cost of capital and NPV for both the projects are positive. Positive NPV will add value to the firm.