Question

1. In 5 years you will get $310. What is the present value if it is invested at

1. 10%

2. 15%

2. You have $450 today. How much will you get if you invest is for 7 years at

1. 10%

2. 15%

3. You want $590 each year for the next 20 years. How much do you need to invest today a

1. 10%

2. 15%

4. What is the NPV of a $200 investment that returns $40 per year for 7 years AND do you accept this investment? Use 12% RRR.

5. What is the NPV of a $200 investment that returns $40 per year for 7 years and has a salvage value of $20 AND do you accept this investment? Use 12% RRR.

6. What is the NPV of a $200 investment with the following cash flows: Yr 1 $20, Yr 2 $40, Yr 3 $45, Yr 4 $50, Yr 5 $45, Yr 6 $40, Yr 7 $40? Use 8% RRR.

7. What is the NPV of a $200 investment with the following cash flows: Yr 1 $20, Yr 2 $40, Yr 3 $45, Yr 4 $50, Yr 5 $45, Yr 6 $40, Yr 7 $40? There is a salvage value of $20. Use 8% RRR.

8. What is the NPV of a $200 investment with the following cash flows: Yr 1 $20, Yr 2 $40, Yr 3 $45, Yr 4 $50, Yr 5 $45, Yr 6 $40, Yr 7 $40? There is a salvage value of $20. Use 9% RRR.

9. You are considering an investment of $200 that pays you $40 per year for 6 years. Your RRR is 8%. What is the approximate IRR AND do you accept this investment?

10. You are considering a $200 investment with the following cash flows: Yr 1 $20, Yr 2 $40, Yr 3 $45, Yr 4 $50, Yr 5 $60. What is the payback period for this investment?

Answer 1

1. In 5 years $310, Present Value:-

a) 10% - $310*PVF(10%,5years)= $310*0.621 = $192.48

b)15% - $310*PVF(15%,5years)= $310*0.497 = $154.12

2.Future Value of $450, invested for 7Years

a) 10%- $ 450*(1+r)^t = $450*(1+.10)⁷ = $450*1.949 = $876.92

b) 15%- $ 450*(1+r)^t = $450*(1+.15)⁷ = $450*2.66 = $1197.08

3. $590 Each year for 20 years, Present Value of Annuity to be calculaed as follows:-

a) 10%- Amount*(1-(1+R)^-20/R)= $590*(1-(1+.10)^-20/0.10) = $5023

b) 15%- Amount*(1-(1+R)^-20/R)= $590*(1-(1+.15)^-20/0.10) = $5539.51

4. Invest ment $200 and Annual return of $40 for 7years

-$200+$40*PVAF(12%,7Years)

-$200+$40*4.564

-200+182.56 = -$17.44

Since NPV nagative we do not accept it.

If salvage Value will be $20 then the NPV:-

-$200+$40*PVAF(12%,7Years) + $20*PVF(12%, 7th year)

-$200+$40*4.564+20*0.452

-200+191.60 = -8.4

Since NPV nagative we do not accept it.

5. Investment of $200 and Different Annual Cash Flow

Year	Cash Flow	Present value Factor @8%	Present Value
0	-200	1	-200
1	20	0.925	18.5
2	40	0.857	34.28
3	45	0.794	35.73
4	50	0.735	36.75
5	45	0.68	30.6
6	40	0.63	25.2
7	40	0.583	23.32
		Total	4.38

Npv Positive we can Accept the project.

If in addition to above salvage value of $20 at 7th year

Year	Cash Flow	Present value Factor @8%	Present Value
0	-200	1	-200
1	20	0.925	18.5
2	40	0.857	34.28
3	45	0.794	35.73
4	50	0.735	36.75
5	45	0.68	30.6
6	40	0.63	25.2
7	60	0.583	34.98
		Total	16.04

Npv Positive we can Accept the project.

If IRR @9%

Year	Cash Flow	Present value Factor @9%	Present Value
0	-200	1	-200
1	20	0.917	18.34
2	40	0.841	33.64
3	45	0.772	34.74
4	50	0.708	35.4
5	45	0.65	29.25
6	40	0.596	23.84
7	60	0.547	32.82
		Total	8.03

Investment $200 and Annual return of $40 for 6years

Trial And Error method:-

@6% = -$200+$40*PVAF(6%,6Years) = -200+196.69 = -3.31

@5%= -$200+$40*PVAF(5%,6Years) = -200+203.02 = 3.02

Interepolation

5%+(1%/+3.02+3.31)*3.02 =5.47%

Since the RRR is higher than the IRR , we do not accept

6. Payback Period

Year	Cash Flow	Cumelative	Present value Factor @9%	Present Value
0	-200	-180	1	-180
1	20	-160	0.917	-146.72
2	40	-120	0.841	-100.92
3	45	-75	0.772	-57.9
4	50	-25	0.708	-17.7
5	60	35	0.65	22.75

Step 1: We must pick the year in which the outflows have become positive. In other words, the year with the last negative outflow has to be selected. So, in this case, it will be year 4.

Step 2: Divide the total cumulative flow in the year in which the cash flows became positive by the total flow of the consecutive year.

So that is: 17.7/35 = 0.5057

Step 3: Step 1 + Step 2 = The payback period is 4.5057 years.