Question

Assume that you are the chief financial officer at Porter Memorial Hospital. The CEO has asked to to analyze two proposed capital investments ----Project X and Project Y. Each project requires a net investment outlay of $10,000, and the cost of capital for each project is 12%. The projects’ expected net cash flows are;
Year Project X Project Y
0 ($10,000) ($10,000)
1 6,500 3,000
2 3,000 3,000
3 3,000 3,000
4 1,000 3,000

Question; Calculate each project’s payback period, net present value, and internal rate of return.

Answer 1

Answer:

Explanation:

Cost of Capital 12%  

Project X      

Year                              0           1              2             3            4

Cah flow                    (10000)   6500   3000     3000     1000  

Discount Factor 12%     1 0.8929 0.7972   0.7118  0.6355

Present Value (10000) 5804 2392 2135 636  

Net Present Value  2.85 years  

Net Present Value  966      

Discount Factor 10% 1 0.9091 0.8264 0.7513 0.6830

Present Value (10000) 5909 2479 2254 683  

Net Present Value          1325      

IRR = Lower rate + $\frac{Lower rate NPV}{Lower rate NPV - Higher rate NPV}$( higher rate - lower rate)

IRR = 0.10 + $\frac{1325}{1325 - 966}$ (0.12-0.10) = 17.38%

Project Y      

Year                              0            1              2          3            4

Cash flow     (10000) 3000 3000  3000  3000  

Discount Factor        1 0.8929 0.7972 0.7118 0.6355

Present Value (10000) 2679   2392   2135  1907  

Payback                 Above 4 years    

Net Present Value   (888)    

Discount Factor 10% 1 0.9091 0.8264 0.7513 0.6830

Present Value (10000)    2727     2479       2254     2049

Net Present Value   (490)    

IRR = Lower rate + ( higher rate - lower rate)

IRR = 0.10 + $\frac{-490}{-490 -(-888)}$ (0.12-0.10) = 7.54%