Question

An investment project costs $12,900 and has annual cash flows of $3,000 for six years.

  

Required :
(a)	What is the discounted payback period if the discount rate is zero percent?
	(Click to select)  4.39  4.21  4.65  3.95  4.3

  

(b)	What is the discounted payback period if the discount rate is 3 percent?
	(Click to select)  4.33  4.68  4.77  4.58  5.03

  

(c)	What is the discounted payback period if the discount rate is 21 percent?
	(Click to select)  Never  3.98  1.02  3.35  4.35

Answer 1

Answer to a

Given the Discount Rate of 0% we have the below formula

Payback Period = Initial Investment / Annual Cash Inflow

Payback Period = 12900/4300 = 4.3

Answer to b

Given the Discount Rate of 3%

Let us first Compute the Present Values of Cash Inflow using the formula = Cash Inflow / (1+R)^n where R is the Discount Rate and N is the No. of Years

Years	Cash Inflow (A)	Discount Factors (B)	Derivation of Discounted Factors (B)	Discounted Cash Flow (AxB)	Cumalative Discounted Cash Flow
Year 0	-12900	1.0000	=1/1.03^0	-12,900	-12,900
Year 1	3000	0.9709	=1/1.03^1	2,913	-9,987
Year 2	3000	0.9426	=1/1.03^2	2,828	-7,160
Year 3	3000	0.9151	=1/1.03^3	2,745	-4,414
Year 4	3000	0.8885	=1/1.03^4	2,665	-1,749
Year 5	3000	0.8626	=1/1.03^5	2,588	839
Year 6	3000	0.8375	=1/1.03^6	2,512	3,352

Year No. in which the Cumalative Cash Flow is Last Negative (A) = Year 4

Cumalative Cash Flow at the end of above year (B) = $ 1749

Total Cash Flow of the year in following A (C) = $ 3000

Therefore Payback Period = A + B / C  

Payback Period = 4 + 1749 / 3000 = 4.58 Years

Answer to c

Given the Discount Rate of 21%

Let us Compute the discounted Cash Flows

Years	Cash Inflow (A)	Discount Factors (B)	Derivation of Discount Factors (B)	Discounted Cash Flow (AxB)	Cumalative Discounted Cash Flow
Year 0	-12900	1.0000	=1/1.21^0	-12,900	-12,900
Year 1	3000	0.8264	=1/1.21^1	2,479	-10,421
Year 2	3000	0.6830	=1/1.21^2	2,049	-8,372
Year 3	3000	0.5645	=1/1.21^3	1,693	-6,678
Year 4	3000	0.4665	=1/1.21^4	1,400	-5,279
Year 5	3000	0.3855	=1/1.21^5	1,157	-4,122
Year 6	3000	0.3186	=1/1.21^6	956	-3,166

We see that the Cumalative discounted cash flows never turn positive. Payback period is the time period in which the initial investment amount will be recouped through the cash flows of the project. We see that when the cash flows of the project are discounted at 21%, the intial investmnet amount is not recouped throghout the life of asset. Therefore the correct answer is never