Question

Pharoah Manufacturing Co. is evaluating two projects. The company uses payback criteria of three years or less. Project A has a cost of $901,000, and project B’s cost is $1,268,100. Cash flows from both projects are given in the following table. Year Project A Project B 1 $86,212 $586,212 2 313,562 413,277 3 427,594 231,199 4 285,552 What are their discounted payback periods? (Round answers to 2 decimal places, e.g. 15.25. If discounted payback period exceeds life of the project, enter 0.00 for the answer.) Discounted payback period of project A 0.00 Discounted payback period of project B 0.00 Which will be accepted with a discount rate of 8 percent? Pharoah should choose

Please show not using excel or financial calculator functions

Answer 1

First of all let us put the given data in tabular format:

Project A has a cost of and project B’s cost is . Cash flows from both projects are given in the following table. Year Project A Project B 1 2 3 231,199 4

Year	Project A	Project B
0	-$901,000,	-$1,268,100
1	$86,212	$586,212
2	313,562	413,277
3	427,594	231,199
4	285,552	0

Following are the discounted CF for the projects:

Project A:

Year	CF	Discount Factor		Discounted CF
0	$        -9,01,000.00	1/(1+0.08)^0=	1	1*-901000=	$        -9,01,000.00
1	$             86,212.00	1/(1+0.08)^1=	0.925925926	0.925925925925926*86212=	$             79,825.93
1	$          3,13,562.00	1/(1+0.08)^1=	0.925925926	0.925925925925926*313562=	$          2,90,335.19
3	$          4,27,594.00	1/(1+0.08)^3=	0.793832241	0.79383224102017*427594=	$          3,39,437.90
4	$          2,85,552.00	1/(1+0.08)^4=	0.735029853	0.735029852796453*285552=	$          2,09,889.24

Project B:

Year	CF	Discount Factor		Discounted CF
0	$      -12,68,100.00	1/(1+0.08)^0=	1	1*-1268100=	$      -12,68,100.00
1	$          5,86,212.00	1/(1+0.08)^1=	0.925925926	0.925925925925926*586212=	$          5,42,788.89
2	$          4,13,277.00	1/(1+0.08)^2=	0.85733882	0.857338820301783*413277=	$          3,54,318.42
3	$          2,31,199.00	1/(1+0.08)^3=	0.793832241	0.79383224102017*231199=	$          1,83,533.22

Now we will calculate the discounted PV for the projects:

Project A:

Year	Opening Balance	Investment	DCF	Closing Balance
0		$   9,01,000.00		$     9,01,000.00
1	$9,01,000.00		$79,825.93	$     8,21,174.07
2	$8,21,174.07		$2,90,335.19	$     5,30,838.89
3	$5,30,838.89		$3,39,437.90	$     1,91,400.99
4	$1,91,400.99		$2,09,889.24	$       -18,488.26

• Opening balance= previous year's closing balance
• Closing balance = opening balance+investment-DCF

We see that at the end of year 3 the closing balance is $1,91,400.99 while the DCF in year 4 is $2,09,889.24 therefore sometime during the year the entire closing balance was recovered. We assume that it is earned uniformly throughout the year therefore the time take is 1,91,400.99/2,09,889.24 = 3.91 years

Project B:

Year	Opening Balance	Investment	Principal repayment	Closing Balance
0		$   12,68,100.00		$   12,68,100.00
1	$      12,68,100.00		$               5,42,788.89	$     7,25,311.11
2	$        7,25,311.11		$               3,54,318.42	$     3,70,992.70
3	$        3,70,992.70		$               1,83,533.22	$     1,87,459.48
4	$        1,87,459.48		$                                  -	$     1,87,459.48

• Opening balance= previous year's closing balance
• Closing balance = opening balance+investment-DCF

We see that at the end of year 3 the closing balance is $1,87,459.48 while the DCF in year 4 is $0 therefore the closing balance was not recovered

As neither of the project has the discounted payback period of less than 3, none meets the criteria