Question

QUESTION 1 Star Industries is considering three alternative projects for the company's investment. The cash flows for three independent projects are as follows: Year 1 Project A ($50,000) $10,000 $15,000 $20,000 $25,000 $30,000 Project B ($100,000) $25,000 $25,000 $25,000 $25,000 $25,000 Project C ($450,000) $200,000 $200,000 $200,000 a) If the discount rate for all three projects is 9.5 percent, calculate the profitability index (PI) of these three projects. Which project will be accepted if the projects are mutually exclusive? b) Calculate the payback period for each project. If Star Industries has a four years payback policy, which project will be accepted? Assume the three projects are independent. c) Given the discount rate of all projects is 9.5 percent, determine the discounted payback period for each project. If Star Industries maintain its four years payback policy, which project will be accepted? Assume the three projects are independent.

Answer 1

Profitability index can be determined using the following formula

$\large PI = \frac{PV of Future cash flow}{Initial Investment}$

Project A. Determine the PV of Future cash flow

PV = 10,000(P/A,9.5%,5) + 5,000(P/G,9.5%,5)

= 10,000*3.8397087 + 5000*6.98495

= $ 73,321.85

$\large PI_A = \frac{73,321.85}{50,000}$

$\large PI_A = 1.47$

Now calculate the PI of project B.

PV = 25,000(P/A,9.5%,5) = 25,000*3.8397087 = $ 95,992.72

$\large PI_B = \frac{95,992.72}{100,000} = 0.96$

Since, PI is less than 1. Reject project B.

Calculating PI of project C

PV = 200,000(P/A,9.5%,3) = 200,000*2.5089 = $ 501,781.37

01,781.37 - 1.12 450,000

Profitability index of project A is higher than Project C. Hence, project A must be selected.

B.

Payback period of project A

$\large PBP_A = 3 + \frac{5000}{25000} = 3.2 years$

Payback period of project B = 4 years

Payback period of project C

$\large PBP_C = 2 + \frac{50000}{200000} = 2.25 years$

All the projects must be selected as all projects have a payback period less than equal to four years.

C. Refer the attached picture for Project A

YrCF 0 -50000 110000 |9132.420091 -40867.5799 215000 12510.16451 -28357.4154 3 20000 15233.07703 -13124.3384 4 25000 17389.35734| 4265.018964 5 30000 19056.8299623321.84892 Dis CF Cumulative CF 50000 50000

$\large DPBP_A = 3 + \frac{13,124.34}{17,389.36} = 3.75 years$

Now for project B discounted payback period will be greater than 5. Or we can say the amount cannot be recovered under project B. Refer the attached picture

CF Yr 0 -100000-100000 1 25000 22831.05023 -77168.9498 225000 20850.27418 -56318.6756 3 25000 19041.34628 -37277.3293 4 25000 17389.35734-19887.972 5 25000 15880.69163-4007.28034 Dis CFCumulative CF 100000

As we can see the cumulative cash flow in 5th year is negative. Thus, this projects Discounted cash flow is more than 5 years.

Project C. First determine the discounted cash flow then the cumulative cash flow as shown in the picture below

Dis CF Cumulative CF CF 450000 0-450000-450000 1 200000 182648.4018 -267351.598 2200000 166802.1934-100549.405 3 200000 152330.7703 51781.36555

$\large DPBP_C= 2 + \frac{100,549.40}{152,330.77} = 2.66 years$

Project A and C will be accepted.

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