Question

City Hospital, a nonprofit organization, estimates that it can save $28,000 a year in cash operating costs for the next 10 years if it buys a special-purpose eyetesting machine at a cost of $110,000. No terminal disposal value is expected. City Hospital’s required rate of return is 14%. Assume all cash flows occur at year-end except for initial investment amounts. City Hospital uses straight-line depreciation.

Calculate the following for the new computer system:

a. Net present value

b. Payback period

c. Internal rate of return

d. Accrual accounting rate of return based on the net initial investment (assume straight-line depreciation)

Answer 1

Answer a)

Calculation of Net Present value

Net Present Value = Present value of savings in Cash operating costs – Purchase price of machine

                                   = (Annual savings in cash operating costs X Present value of annuity factor at 14% for 10 years) – Purchase price of machine

                                    = ($ 28,000 X 5.21612) - $ 110,000

                                    = $ 146,051 - $ 110,000

                                    = $ 36,051

Therefore the Net Present value is $ 36,051.

Answer b)

Calculation of Payback Period

Payback Period = Purchase price of machine/ Annual Savings in operating costs

                             = $ 110,000/ $ 28,000

                             = 3.9286 years

Therefore payback period is 3.9286 years

Answer c)

Calculation of Internal rate of return

Internal rate of return is the rate at which the present value of cash inflows is equal to the present value of cash outflows. The internal rate of return can be calculated by computing the approximate present value of annuity of $ 1.

Approximate Present value of annuity $ 1 = Purchase price of machine/ Annual Savings in operating costs

                                                                                  = $ 110,000/ $ 28,000

                                                                                  = 3.92857

On a perusal of present value of annuity of $ 1 table, the present value of annuity of $ 1 at 21% for 10 years is 4.05408 and at 22% is 3.92318. Therefore, the IRR lies between 21% and 22%

Internal rate of return = 21% + (4.05408 – 3.92857)/ (4.05408 – 3.92318)

                                          = 21% + 0.12551/0.1309

                                           = 21.96%

Therefore internal rate of return is 21.96%.

  

Answer d)

Calculation of Accrual Accounting rate of return

Accrual Accounting rate of return = Average Annual Net Income/ Initial investment

                                                             = $ 17,000/ $ 110,000

                                                              = 15.45%

Working Notes:

Working Note:

Calculation of Annual depreciation expense

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

                                                                     = ($ 110,000 - $ 0)/ 10 years

                                                                     = $ 11,000

Calculation of Annual Net Income:

Annual Net Income = Annual savings in cash operating costs – Annual depreciation expense

                                    = $ 28,000 - $ 11,000

                                    = $ 17,000