Corporate Finance (The Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
Corporate Finance (The Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
11th Edition
ISBN: 9780077861759
Author: Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor
Publisher: McGraw-Hill Education
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Chapter 4, Problem 48QP
Summary Introduction

To compute: The present value of annuity.

Purchasing Power:

It refers to the ability of the currency to buy something. Purchasing power decreases with increase in inflation and increase with decrease in inflation.

Expert Solution & Answer
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Explanation of Solution

Given,

Annuity is of 5 years.

Semi annual payments are of $6,175.

Discount rate is 11%.

Semiannual rate is 5.054%.

Formula to calculate present value of annuity,

PVA=Semiannualpayment[1(11+semiannualrate)10semiannualrate]

Where,

  • PVA is present value of annuity.

Substitute $6,175 for semiannual payment, and 5.054% for semi annual rate,

PVA=$6,175[1(11.055)100.055]=$6,175[10.58500.055]=$6,175[0.41500.055]=$46,592.84

Hence, the present value of annuity is $46,592.84.

Effective annual rate is 11.48%.

Given, number of years is 4.

Formula to calculate present value of annuity for 5 years,

PVA=TotalPVA(1+Effectiveannualrate)Numberofyear

Where,

  • PVA means present value of annuity.

Substitute $46,592.84 for total PVA, 5.5% for effective annual rate and 4 for number of years.

PVA=$46,592.84(1+0.055)4=$46,592.84(1.2388)=$37,610.52

Hence, the present value of annuity of 5 years is $37,610.52.

Compute present value of annuity for 3 years.

Number of years that will be taken is 6.

Formula to calculate present value of annuity for 3 years,

PVA=TotalPVA(1+Effectiveannualrate)Numberofyear

Where,

  • PVA means present value of annuity.

Substitute $46,592.84 for total PVA, 5.5% for effective annual rate and 6 for number of years.

PVA=$46,592.84(1+0.055)6=$46,592.84(1.3788)=$33,791.26

Hence, the present value of annuity of 3 years is $33,791.26.

Compute present value of annuity for current year.

Number of years that will be taken is 9.

Formula to calculate present value of annuity for current year,

PVA=TotalPVA(1+Effectiveannualrate)Numberofyear

Where,

  • PVA is present value of annuity.

Substitute $47,154.54 for total PVA, 5.5% for effective annual rate and 9 for number of years.

PVA=$46,592.84(1+0.055)9=$46,592.84(1.6190)=$28,778.78

Hence, the present value of annuity of 3 years is $28,778.78.

Working Note:

Computation of monthly rate,

Monthlyrate=RateNumberofmonths=0.1112=0.0091

Hence, the monthly rate is 0.0091.

Computation of semi annual rate,

Semiannualrate=(1+Monthlyrate)61=(1+0.0091)61=1.0551=5.5%

Hence, the semiannual rate is 5.5%.

Computation of early annual rate,

Effectiveannualrate=(1+0.0091)121=(1.0091)121=1.11481=0.1148

Hence, the effective annual rate is 11.48%.

Hence, the present value annuity for 5 years, 3 years and currently is $37,610.52, $33,791.26 and $28,778.78.

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Chapter 4 Solutions

Corporate Finance (The Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)

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