Question

Anita Flores has a very successful bake shop in the center of town. She wishes to evaluate the feasibility of investing $95,000 in a new oven that has a five year life. She has estimated the cash inflows associated with the proposal as shown in the following table. The business has a 12% cost of capital.

Year	Cash Inflows
1	$20,000
2	$25,000
3	$30,000
4	$35,000
5	$40,000

            Question:

1. Calculate the payback period for the proposed investment.
2. Calculate the internal rate of return (IRR) rounded to the nearest whole percent for the proposed project. (Because we do not use financial calculators, determine the range between the higher and the lower whole percent).
3. Evaluate the acceptability of the proposed investment using NPV and IRR. What do you recommend?

Answer 1

Payback period calculation

Year	Cash inflow	Cumulative cash inflow
1	$20,000	20,000
2	$25,000	45,000
3	$30,000	75,000
4	$35,000	1,10,000
5	$40,000	15,0,000

Initial investment = $95,000

Payback period = Y + B / C

Y = No; of years immediately preceding the year of final recovery

B = Balance amount still to be recovered

C = Cash inflow during the year of final recovery

Payback period = 3 + (95,000 - 75,000) / 35000

= 3 + 20000 / 35000

= 3 +0.57

=3.57 years

Internal rate of return [ IRR]

Trial and error method:

first let's take 13% as NPV for checking weather get positive or negative value

NPV = Cash flow / ( 1 + r )1 + Cash flow / ( 1 + r )2 + Cash flow / ( 1 + r )n​​​​​​​ - initial investment

NPV = 20,000/ ( 1+0.13) + 25,000/(1+0.13)2 + 30,000/ (1 + 0.13)3 +35,000 / (1+0.13)4 + 40,000/ (1+0.13)5 - 95,000

= (17,699.11 + 19,578.66 + 20,791.50 +21,466.15 + 21,710.39 ) - 95,000

= 1,01,245.84 - 95,000

= $ 6,254.84

NPV ,discount rate @ 16%

NPV = 20,000/ ( 1+0.16) + 25,000/(1+0.16)2 + 30,000/ (1 + 0.16)3 +35,000 / (1+0.16)4 + 40,000/ (1+0.16)5 - 95,000

= (17,241.37 + 18579.07 + 19,219.73 + 19330.18 + 19,044.52 ) - 95,000

= 93,414.89 - 95,000

= - 1585.11

IRR = A + [( C - O ) / ( C - D ) ] * ( B - A)

A = lowest discount rate value

C - O = lowest discount rate cash flow - initial investment

C - D = lowest discount rate cash flow - higher discount rate cash flow

IRR = 13 % + [( 6,254.84) / (1,01,245.84 - 93,414.89 ) * ( 16% - 13 % )

= 13 % +[ 6,254.84 / 7830.95] * 3%

= 13 % +( 0.7987 * 3)

= 13 + 2.39

= 15.39%

Here we got IRR as 15.39 %, it may be very littile point difference from the accurate value. eventhough it is the IRR

NPV and IRR should be implemented for the project. it meets the decision criteria