Question

BASIC INTERNAL RATE OF RETURN ANALYSIS

Smokey Thomas, owner of Steam Whistle Company, was approached by a local dealer of air- conditioning units. The dealer proposed replacing Stream Whistle's old cooling system with a modern, more efficient system. The cost of the new system was quoted at $96,660, but it would save $20,000 per year in energy costs. The estimated life of the new system is 10 years, with no salvage value expected. Excited over the possibility of saving $20,000 per year and having a more reliable unit, Smokey requested an analysis of the project's economic viability. All capital projects are required to earn at least the firm's cost of capital, which is 10 percent. There are no income taxes.

Required:

1. Calculate the project's IRR. Should the company acquire the new cooling system?

2. Suppose that energy savings are less than claimed. Calculate the minimum annual cash savings that must be realized for the project to earn a rate equal to the firm's cost of capital.

3. Suppose that the life of the new system is overestimated by two years. Repeat Requirements 1 and 2 under this assumption.

4. Explain the implications of the answers from Requirements 1, 2, and 3.

Answer 1

Answer is given below

a) Calculation of IRR Year Total Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 (Outflow) Inflow Cash outfloy Cash inflow Cash inflow Cash inflow Cash inflow Cash inflow Cash inflow Cash inflow Cash inflow Cash inflow Cash inflow oo -$96,660 $20,000 $20,000 $20,000 $20,000 $20,000 $20,000 $20,000 $20,000 $20,000 $20,000 16% Year 6 Year 7 Year 8 Year 9 Year 10 IRR Since IRR is above cost of capital 10% the project should be accepted Calculation of NPV Initial investment Annual cash inflow PV factor $96,660 $20,000 6.1446 PV of cash inflows Less: Investment Net present value $122,891 $96,660 $26,231 b) Cost of Machine Present value factor $96,660 6.1446 10 years Annual savings | $15,731 10 years At above annual savings IRR is equal to cost of capital c) Calculation of IRR Year Total Year 0 Year 1 Year 2 Year 3 (Outflow) Inflow Cash outflow Cash inflow Cash inflow Cash inflow Cash inflow Cash inflow Cash inflow Cash inflow Cash inflow Year 4 Year 5 Year 6 Year 7 Year 8 IRR $96,660 $20,000 $20,000 $20,000 $20,000 $20,000 $20,000 $20,000 $20,000 13% Since IRR is above cost of capital 10% the project should be accepted Calculation of NPV Initial investment Annual cash inflow PV factor $96,660 $20,000 5.3349 PV of cash inflows Less: Investment Net present value $106,699 $96,660 $10,039 Cost of Machine Present value factor $96,660 5.3349 8 years Annual savings | $18,118 8 years At above annual savings IRR is equal to cost of capital d) IRR is cost of capital at which Present value of cash inflows will be equal to present value of cash outflows Hence any project having IRR above cost of capital will be accepted When estimated life of cash flow is reduced by 2 years IRR will decrease and also the net present value