Question

Problem 25-03A Brooks Clinic is considering investing in new heart-monitoring equipment. It has two options. Option A would have an initial lower cost but would require a significant expenditure for rebuilding after 4 years. Option B would require no rebuilding expenditure, but its maintenance costs would be higher. Since the Option B machine is of initial higher quality, it is expected to have a salvage value at the end of its useful life. The following estimates were made of the cash flows. The company's cost of capital is 5%. Option A Option B Initial cost $169,000 $291,000 Annual cash inflows $70,400 $82,500 Annual cash outflows $31,000 $25,400 Cost to rebuild (end of year 4) $48,600 $0 $0 Salvage value $7,200 7 years 7 years Estimated useful life Click here to view the factor table. Compute the (1) net present value, (2) profitability index, and (3) internal rate of return for each option. (Hint: To solve for internal rate of return, experiment with alternative discount rates to arrive at a net present value of zero.) (If the net present value is negative, use either a negative sign preceding the number eg -45 or parentheses eg (45). Round answers for present value and IRR to 0 decimal places, e.g. 125 and round profitability index to 2 decimal places, e.g. 12.50. For calculation purposes, use 5 decimal places as displayed in the factor table provided.)

Answer 1

Answer:

a. 1. Net Present Value:

Option A:

Present Value Factor of 5% of 7th Year PVIF(5%,7) = 0.71068

Present Value Factor of 5% for 7 Years PVAF(5%,7) = 5.7864

Present Value of Cash Outflows = (Annual Cash Inflows - Annual Cash Outflows)*PVAF(5%,7)

= ($ 70400 - $ 31000)*5.7864 - ($ 48600*0.82270)

= $ 227984.16 - $ 39983.22

= $ 188000.94

Present Value of Initial Investement = $ 169000*1

=$ 169,000

Net Present Value of Option I = $ 188000.94 - $ 169,000

= $ 19000.94

Option B:

Present Value Factor of 5% of 7th Year PVIF(5%,7) = 0.71068

Present Value Factor of 5% for 7 Years PVAF(5%,7) = 5.7864

Present Value Of Salvage Value = $ 7200*0.71068

= $ 5116.896

Present Value of Cash Outflows = (Annual Cash Inflows - Annual Cash Outflows)*PVAF(8%,7)

= ($ 82500- $ 25400)*5.7864

= $ 330403.44

Present Value of Initial Investement = $ 291000*1

=$ 291,000

Net Present Value of Option I = $ 330403.44 + $ 5116.896 - $ 291000

= $ 44520.34

2. Profitability Index:

Formulae = Discounted Cash Flows / Cash Outlay

Option A: $ 19000.94 + $ 169000 / $ 169000 = 1.11

Option B: $ 44520.34 + $ 291000 / $ 291000 = 1.15

3. Imternal Rate of Return:

First Lets Calculate Pay back Period and then determine IRR for both the Options by trial and error method.

Option A: Payback Period = Cash Outflow / Annual Cash Inflows = $ 169,000/ ($ 70400 - $ 31000)

= $ 169000 / $ 39400

= 4.29 Years

Now when seen at the Present Value Annuity Table, for 7 Years we need to select the two figures one of which must be more than 4.29 and the other lesser than 4.29 So, we will get 14% (4.288) and 15% (4.160)

So, IRR = 14% + (4.288-4.29)/(4.288-4.160)*(15%-14%)

= 14% + (0.002/0.128)*1

= 14% + 0.02%

= 14.02%

Option B: Payback Period = Cash Outflow / Annual Cash Inflows = $ 291000 / ($ 82500 - $ 25400)

= $ 291000 / $ 57100

= 5.11 Years

Now when seen at the Present Value Annuity Table, for 7 Years we need to select the two figures one of which must be more than 5.11 and the other lesser than 5.11 . So, we will get 8% (5.206) and 9% (5.033)

So, IRR = 8% + (5.206-5.11)/(5.206-5.033)*(9%-8%)

= 8% + (0.096/0.173)*1

= 8% + 0.5549%

= 8.5549%

b. Based on NPV, we would select Option B

Based on Profitability Index, we would select Option B and hence we would be option Option B