Question

YR 0	Yr 1	Yr 2	Yr 3	Yr 4	Yr 5	Yr 6	Yr 7	Yr 8
(210,000,000)	31,672,290	39,228,131	39,567,278	41,201,345	43,933,136	48,748,924	54,154,462	166,129,332

Calculate discounted payback. Please show steps

Answer 1

Payback period = 5.30 years.

When the annual cash flows are not uniform, the cumulative cash inflows from operations must be calculated for each year. The payback period shall be corresponding period when total of cumulative cash inflows is equal to the initial capital investment. However, if exact sum does not match then the period in which it lies should be identified. After that we need to compute the fraction of the year.

Initial capital investment = $210,000,000

Since Discount rate is not provided in the question, cash flows provided in the question is considered as discounted cash flows

Cash flows

Year	Discounted Cash flow	Cumulative cash flow
1	$      31,672,290.00	$    31,672,290.00
2	$      39,228,131.00	$    70,900,421.00
3	$      39,567,278.00	$ 110,467,699.00
4	$      41,201,345.00	$ 151,669,044.00
5	$      43,933,136.00	$ 195,602,180.00
6	$      48,748,924.00	$ 244,351,104.00
7	$      54,154,462.00	$ 298,505,566.00
8	$    166,129,332.00	$ 464,634,898.00

Payback period in this case will lie between year 5 and year 6.

Since up to 5 years a sum of $195,602,180 shall be recovered, balance of $14,397,820 shall be recovered in the part (Fraction) of 6^th year, Computation is as follows

            = (Balance recoverable ÷ Cash flow of year 6)

= $14,397,820 ÷ $ 48,748,924

=0.2953

            = 0.30 years (rounded)

Payback period = 5.30 years (rounded)

Amount of $195,602,180 is recovered in 5 years’ time and amount of $14,397,820 is recovered in 0.30 year therefore total payback = 5.30 years