Question

Merrill Corp. has the following information available about a potential capital investment:   

Initial investment	$	1,800,000
Annual net income	$	200,000
Expected life		8	years
Salvage value	$	240,000
Merrill’s cost of capital		10	%

Assume straight line depreciation method is used.

Required:

1. Calculate the project’s net present value.

2. Without making any calculations, determine whether the internal rate of return (IRR) is more or less than 10 percent.

3. Calculate the net present value using a 15 percent discount rate.

4. Without making any calculations, determine whether the internal rate of return (IRR) is more or less than 15 percent.

Answer 1

Answer 1)

Calculation of Net Present value using 10% discount rate

Net Present value = Present Value of cash inflows – Present value of cash outflows

                                   = $ 2,219,260 - $ 1,800,000

                                   = $ 419,260

Therefore the Net present value of the investment using 10% discount rate is $ 419,260.

Working Note:

Calculation of Annual depreciation expense

Annual depreciation expense = (Original cost – salvage value)/ number of years of useful life of investment

                                                                     = ($ 1,800,000 - $ 240,000)/ 8 years

                                                                     = $ 195,000

Calculation of Annual cash inflow:

Annual cash inflow = Annual net income + Annual depreciation expense

                                    = $ 200,000 + $ 195,000

                                    = $ 395,000            

Calculation of present value of cash inflows using 10% discount rate:

Present value of cash inflows = (Annual cash inflow X Present value annuity factor at 10% for 8 years) + (salvage value X Present value factor at 10% for 8 years)

                                                        = ($ 395,000 X 5.33493) + ($ 240,000 X 0.46651)

                                                        = $ 2,107,297.35 + $ 111,962.40

                                                        = $ 2,219,260 (rounded off)

Answer 2)

Internal rate of return is the rate at which the present value of cash inflows is equal to the present value of cash inflows and Net present value is Zero. At 10% discount rate, the Net present value of the investment is positive (i.e. $ 419,260). It indicates that the Net present value will be zero at a higher discount rate and accordingly, the Internal rate of return is higher than 10%.

Answer 3)

Calculation of Net Present value using 15% discount rate

Net Present value = Present Value of cash inflows – Present value of cash outflows

                                   = $ 1,850,947 - $ 1,800,000

                                   = $ 50,947

Therefore the Net present value of the investment using 15% discount rate is $ 50,947.

Working Note:

Calculation of Annual depreciation expense

Annual depreciation expense = (Original cost – salvage value)/ number of years of useful life of investment

                                                                     = ($ 1,800,000 - $ 240,000)/ 8 years

                                                                     = $ 195,000

Calculation of Annual cash inflow:

Annual cash inflow = Annual net income + Annual depreciation expense

                                    = $ 200,000 + $ 195,000

                                    = $ 395,000            

Calculation of present value of cash inflows using 15% discount rate:

Present value of cash inflows = (Annual cash inflow X Present value annuity factor at 15% for 8 years) + (salvage value X Present value factor at 15% for 8 years)

                                                        = ($ 395,000 X 4.48732) + ($ 240,000 X 0.32690)

                                                        = $ 1,772,491.40 + $ 78,456

                                                        = $ 1,850,947 (rounded off)

Answer 4)

Internal rate of return is the rate at which the present value of cash inflows is equal to the present value of cash inflows and Net present value is Zero. At 15% discount rate, the Net present value of the investment is positive (i.e. $ 50,947). It indicates that the Net present value will be zero at a higher discount rate and accordingly, the Internal rate of return is higher than 15%.