om Alexander has an opportunity to purchase any of the inves

om Alexander has an opportunity to purchase any of the investments shown in the following? table,The purchase? price, the amount of the single cash? inflow, and its year of receipt are given for each investment. Which purchase recommendations would you? make, assuming that Tom can earn? 10% on his? investments?

$5,000 $10,718 7

$150 $1,110 22

$950 $3,280 12

$250 $12,446 42

Solution

Since all the investments options have different investment amount, hence profitablity index method will be most suitable here to evaluate the investment proposals.

(i)

Purchase price = $5,000

Cash inflow = $10,718

Time = 7 years

Present value of cash inflow = Cash inflow x PVF(_{10%, 7})

= 10,718 x 0.513

= $5,498

Profitability index = Present value of cash inflows/ Present value of cash outflows

= 5,498/5,000

= 1.100

(ii)

Purchase price = $150

Cash inflow = $1,110

Time = 22 years

PVF = 1/(1 + r)ⁿ

= 1/(1 + 0.10)²²

= 1/(1.10)²²

= 1/8.14

= 0.123

Present value of cash inflow = Cash inflow x PVF(_{10%, 22})

= 1,110 x 0.123

= $136

Profitability index = Present value of cash inflows/ Present value of cash outflows

= 136/150

= 0.91

(iii)

Purchase price = $950

Cash inflow = $3,280

Time = 12 years

Present value of cash inflow = Cash inflow x PVF(_{10%, 12})

= 3,280 x 0.319

= $1,046

Profitability index = Present value of cash inflows/ Present value of cash outflows

= 1,046/950

= 1.102

(iv)

Purchase price = $250

Cash inflow = $12,446

Time = 42 years

PVF = 1/(1 + r)ⁿ

= 1/(1 + 0.10)⁴²

= 1/(1.10)⁴²

= 1/54.76

= 0.018

Present value of cash inflow = Cash inflow x PVF(_{10%, 22})

= 12,446 x 0.018

= $225

Profitability index = Present value of cash inflows/ Present value of cash outflows

= 225/250

= 0.90

Conclusion- Since profitability index of third investment option is highest, hence third investment proposal should be chosen by Tom