Question

If a project costs ​$130,000 and is expected to return ​$31,500 ​annually, how long does it take to recover the initial​ investment? What would be the discounted payback period at i=14​% Assume that the cash flows occur continuously throughout the year. The payback period is nothing years. ​(Round to one decimal​ place.)The discounted payback period at i=14​% would be nothing years

Answer 1

To calculate discounted payback period we will first calculate the present value of cash flows at interest rate of 14% along with cumulative cash flows for all the years.

Discount rate = (1/1+i)ⁿ

Where,

i = interest rate

n = number of years

Year	Cash flow	Discount rate@14%	PV of cash flow	Cumulative PV of cash flow
1	31500	0.8772	27631.8	27631.8
2	31500	0.7695	24239.25	51871.05
3	31500	0.6750	21262.5	73133.55
4	31500	0.5921	18651.15	91784.7
5	31500	0.5194	16361.1	108145.8
6	31500	0.4556	14351.4	122497.2
7	31500	0.3996	12587.4	135084.6

Discounted payback period = Years before full recovery +( unrecovered cost during the starting of the Year / cash flow during the year)

Unrecovered cost during the starting of the year = 130000 - 122497.2 = 7502.8

Therefore,  

Discounted payback period = 6 +(7502.8/12587.4)

= 6.6 years