show all steps Question1 The following infinite cash flow has a 15% internal rat

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Question1 The following infinite cash flow has a 15% internal rate of return (IRR). Compute the unknown value of X $2000 $2000 $2,000 $2,000 Years Repeating pattern $16,205 (8 marks) Question 2 Consider the following financial data for a project Initial investment, $4,000 Project life, years Salvage value, S Annual revenue, S 5,229 Annual expense, $ 3,000 2 0 (a) What is the IRR for this project? (b) If annual expense increases at a 7% rate over the previous year's expenses, at what annual rate would annual income have to increase to maintain the same IRR obtained in (a)? (12 marks)

Explanation / Answer

Ans 1)

IRR is the rate that makes Net Present Worth of Investment equals to zero

16205=2000/(1+IRR)+2000/(1+IRR)^2+X/(1+IRR)^3+X/(1+IRR)^4+2000/(1+IRR)^5+2000/(1+IRR)^6+X/(1+IRR)^7+X/(1+IRR)^8

IRR =15%

16205=2000/(1+15%)+2000/(1+15%)^2+X/(1+15%)^3+X/(1+15%)^4+2000/(1+15%)^5+2000/(1+15%)^6+X/(1+15%)^7+X/(1+15%)^8

X=$5742

Ans B)

Internal rate of Return is interest rate that makes Net Present Value equals to zero

NPV=PW of Benefits-PW of Costs

PW of Benefits=PW of Revenue+PW of Salvage Value

PW of Revenue=5229+5299/(1+IRR)+5299/(1+IRR)^2

PW of Salvage Value=0

PW of Benefits=5229+5299/(1+IRR)+5299/(1+IRR)^2

PW of Costs=4000+3000/(1+IRR)+3000/(1+IRR)^2

5299/(1+IRR)+5299/(1+IRR)^2=4000+3000/(1+IRR)+3000/(1+IRR)^2

2299/(1+IRR)+2299/(1+IRR)^2=4000

(1/(1+IRR)+(1/(1+IRR)^2=4000/2299=1.74

Then IRR=9.5%

Ans b)

If annual expenses increse by 7%

PW of Costs=3000/(1+IRR)+3000(1.07)/(1+IRR)^2+4000

5229/(1+IRR)+5229(1+x)/(1+IRR)^2=4000+3000/(1+IRR)+3000(1.07)/(1+IRR)^2=4000+3000/(1+IRR)+3210/(1+IRR)^2

We need to keep IRR the same and it is equal to 9.5%

5229/1.095+5229(1+x)/(1.095)^2=4000+3000/(1.095)+3210/(1.095)^2

2229/1.095+[5229(1+x)-3210]/(1.095)^2=4000

2035.62+1684+4361x=4000

3719.6+4361x=4000

4361x=280.4

x=280.4/4361;x=6.42%

Therefore Annual income is to be increased by 6.42% each year

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