Question

Chicago hospital, a tax-paying entity, estimates that it can save $30,000 a year in cash operating cost for the next 10 years if it buys a special purpose eye testing machine at a cost of $135,000. No terminal disposal value is expected. Chicago's hospitals required rate of return is 10%. Assume all cash flows occur at year-end except for initial investment amounts. Chicago hospital uses straight-line depreciation. The income tax rate is 34% for all transactions that affect income taxes.

calculate the following for the special purpose eye testing machine

a. Net Present Value

b. Payback period

c. Internal rate of return

d. Accrual accounting rate of return based on net initial investment

e. Accrual accounting rate of return based on average investment

f. How would your computations in requirement 1 be affected if the special-purpose machine had a $15,000 terminal supposed value at the end of 10 years? Assume depreciation deductions are based on the $135,000 purchase cost and zero turn oil disposal value using the straight-line method. Answer briefly in words without further calculations

Answer 1

Initial investment= 135,000

Annual cash flow include the depreciation tax shield and saved cost

Depreciation (straight line, so termination value,for 10 years)= Value of asset / Life of asset= 135,000 / 10= 13,500

in actual Depreciation is not a cash flow. depreciation expense will leads to a tax shield

depreciation tax shield= depreciation * tax rate= 13,500 * 0.34=4590

Cash savings after tax= cash savings *( 1- tax rate)

=30,000 *(1-0.34)= 30,000 * 0.66= 19,800

Total annual after tax cash flow= depreciation tax sheild + after tax cash savings= 4590 + 19,800= 24,390

1. NET PRESENT VALUE (NPV)

NPV= present value of net cash inflow -Initial investment

Annual cash inflow= 24,390

Discount rate = 10%

periods = 10 years

Present value of $1 Annuity at discount rate 10% and period 10 years=6.145

Present value of net cash inflow= Annual cash flow * present value factor

=24,390 * 6.145= 149,876.55

NPV= present value of net cash inflow - initial investment= 149,876.55 - 135,000= 14,876.55

2.Payback periode= initial investment/ annual cash flow= 135,000 /24,390= 5.535 years

3.Internal rate of return is the rate at which NPV = 0

24,390 * present value factor - 135,000=000

so, 24,390 * present value factor = 135,000

present value factor= 135,000/ 24,390= 5.5351

Find 5.5351 in present value of $1 annuity table if periode is 10 years

According to  present value of $1 annuity table if periode is 10 years, 5.5351 is between 12% and 14%

Internal rate of return is aproximately 13%

4.Accounting rate of return based on initial investment= increase in net income / initial investment

increase in income before tax is 30,000 savings less 13,500 depreciation; total 30,000- 13,500=16,500

cash savings is an income and depreciation is an expense in income statement

increase in net income = inrease in income before tax *(1- tax rate)

=16,500*(1-0.34)= 10,890

Accounting rate of return based on initial investment= increase in annual income / initial investment

= 10890 / 135,000= 0.0806667

Accounting rate of return based on initial investment= 0.0806667 * 100= 8.06667%

5.Accounting rate of return based on average investment= increase in income/ average investment

Average investment= initial investment / 2= 135,000 / 2= 67,500

increase in income =10890

.Accounting rate of return based on average investment= increase in income/ average investment= 10890/ 67500=0.161333

Accounting rate of return based on average investment= 0.161333* 100= 16.1333%

6. if the asset have a terminal value at the end of the periode , we should include it in the calculation of present value of future cash inflow.if the machine have 15,000 terminal value at the end of 10 years and the asset depreciated with an assumption of zero salvage value,it will increase total cash flow in year 10

icrease in cash flow in year 10 after tax= 15000 * (1-0.34)= 9,900