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J、Co have heard about the concept of the time value of money. Required: (i) Complete the gaps in the following statement: The time value of money means that $1 now is worth (GAP 1) than $1 in the future. The reasons for this are risk, (Gap 2) and potential for earning a return e.g. interest. (ii) Using a discount rate of 8%, and assuming that the cash flows arise at the end of a year, calculate the discounted payback period.
J、Co have heard about the concept of the time value of money. Required: (i) Complete the gaps in the following statement: The time value of money means that $1 now is worth (GAP 1) than $1 in the future. The reasons for this are risk, (Gap 2) and potential for earning a return e.g. interest. (ii) Using a discount rate of 8%, and assuming that the cash flows arise at the end of a year, calculate the discounted payback period.
【参考答案及解析】
(i) Gap 1 more Gap 2 inflation (ii) Year Cash flow x DF Cumulative cashflow 0 -18,750 -18,750 1 5,000 x 0.926 = 4,630 -14,120 2 5,000 x 0.857 = 4,285 -9,835 3 5,000 x 0.794 = 3,970 -5,865 4 5,000 x 0.735 = 3,675 -2,190 5 5,000 x 0.681 = 3,405 +1,215 As the cash flows arise at the end of the year payback will be 5 years Alternative working The project will payback when $18,750 = $5,000 x AF @ 8% AF(1-n)=3.75 The annuity factor for 4 years is 3.312, and 5 years is 3.993. Therefore the payback must occur at 5 years as the cash flows arise at the end of the year.
(i) Gap 1 more Gap 2 inflation (ii) Year Cash flow x DF Cumulative cashflow 0 -18,750 -18,750 1 5,000 x 0.926 = 4,630 -14,120 2 5,000 x 0.857 = 4,285 -9,835 3 5,000 x 0.794 = 3,970 -5,865 4 5,000 x 0.735 = 3,675 -2,190 5 5,000 x 0.681 = 3,405 +1,215 As the cash flows arise at the end of the year payback will be 5 years Alternative working The project will payback when $18,750 = $5,000 x AF @ 8% AF(1-n)=3.75 The annuity factor for 4 years is 3.312, and 5 years is 3.993. Therefore the payback must occur at 5 years as the cash flows arise at the end of the year.