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# Capital Budgeting: Math Case Study (Answering questions)

High school

Math Problem

Finance & Accounting

Pages 7 (1757 words)

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1. From the given data, it can be seen that Project ‘p’ has a higher NPV as compared to Project ‘q’. Hence, if NPV is chosen as the criterion, Project ‘p’ must be preferred. However, it is also seen that Project ‘q’ has a higher IRR.

## Introduction

Overall, there is a large difference between NPVs of the two projects while there is a smaller difference between their IRRs. Hence, Project ‘p’ should be selected over Project ‘q’.

Moreover, IRR ranking is misleading here because the base investment (initial cash outflow) in the two projects is not the same. The cash outflow in Project ‘p’ ($200) is twice that of project ‘q’ ($100). Hence, it would not be appropriate to compare the two projects on IRR basis.

2. Let ‘S’ be the periodic saving, ‘i’ be the interest rate, ‘P’ be the annual payments to be ensured, ‘n’ be the number of years for which savings are done and ‘N’ be the number of years for which payments are to be ensured. According to the given data,

S has to be calculated

i=4%

P=$30,000

n=20 years

N=15 years

Now, Future value of all savings at the end of 65 years= Present Value of all payments at the end of 65 years

i.e. S[(1+i)^n-1]/i = P (1-(1/(1+i)^N))/i

i.e. S[(1+.04)^20-1]/.04 = 30000 (1-(1/(1+.04)^15))/.04

i.e. S= $11,201.25

Hence, the annual savings must be $11,201.

3. Table 3.1 depicts the Interest paid, Principal Paid and Principal Balance at the end of first 10 years. Here, Interest paid is calculated as 10% of principal balance in the previous year. The Principal paid is calculated as the difference of Yearly Installment and Interest

Table 3.1: Yearly Installment Plan at 10% rate of interest throughout

Year Interest paid Principal paid Principal balance

0 0 0 200000

...

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