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# Market Expension

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Submitted By Othman777
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Problem 1. A client invests \$500,000 in a bond fund project to earn 7% annually. Estimate the value of this investment after 10 years.

Solution

FVN = PV(1+r)N

Here we have FV10= 500,000 * (1+0,07)10 = 983 575,68 Problem 2. For liquidity purposes a client keeps \$100,000 in a bank account. The bank quotes a stated annual interest rate of 7%. How much will your client have in this account at the end a. One year b. Two years Assuming no withdrawals (so all the interest are reinvested) with 1. Quarterly compounding 2. Monthly compounding 3. Continuous compounding Solution a. One year investment 1. Quarterly compounding

FVN = PV*(1+r/m)mN

FVN = 100,000*(1+0,07/4)4x1=107 185,90

2. Monthly compounding FVN = PV*(1+r/m)mN

FVN = 100,000*(1+0,07/12)12x1=107 229,01

3. Contiuous compounding FVN = PV*er

FVN = 100,000*(e)0,07=107 250,82

b. Two years 4. Quarterly compounding FVN = PV*(1+r/m)mN

FVN = 100,000*(1+0,07/4)4x2=114 888,18

5. Monthly compounding FVN = PV*(1+r/m)mN

FVN = 100,000*(1+0,07/12)12x2=114 980,60

6. Contiuous compounding FVN = PV*er

Problem 3. A couple plans to set aside \$20,000 per year in a portfolio that earns 7% a year. If they make their first saving contribution one year from now, how much will they have at the end of 20 years? Solution ⎛ (1 + 0,07) 20 − 1 ⎞ ⎟ = 819909,84 PV = 20000 * ⎜ ⎜ ⎟ 0,07 ⎝ ⎠ Problem 4. To cover the first year’s total college tuition payments for his two children, a father will make a \$75,000 payment five years from now. How much will he need to invest today to meet this payment if the investment earns 6% annually? Solution ⎛ 75000 ⎞ PV = ⎜ ⎜ (1 + 0,06) 5 ⎟ = 56044,36 ⎟ ⎝ ⎠ Problem 5 Two major investment projects each have the same initial capital outlay of \$2,000 million. The expected net revenues on the respective projects over the next 4 years are outlined below (\$ millions)

Year 0 Year 1 Year 2 Year 3 Year 4 Project A -2000 1000 800 600 200 Project B -2000 200 600 800 1200

FVN = 100,000*(e)0,07x2=115 027,38

a. Calculate the payback period for each of the projects Payback period for project A is 3 years since the sum of the cash flows in Year 1,2,3 is bigger then the initial investment (1000 + 800 + 600)= 2400 > 2000 Payback period for project B is 4 years since the sum of the cash flows in Year 1,2,3,4 is bigger then the initial investment (200 + 600 + 800 + 1200)= 2800 > 2000 b. Assuming that the required rate of return is 10% calculate the NPV of each project. Are the project profitable? Which of them would you choose? Project A PV of Cash Flows at the discount rate of 10% is 2157,64 NPV of the project 2157,64 – 2000 = 157,64 Project B PV of Cash Flows at the discount rate of 10% is 2098,35 NPV of the project 2098,35 – 2000 = 98,35 Both projects are profitable since the NPV at the required rate of return of 10% is positive. We should choose the project A since it generates a higher NPV. c. Calculate IRR for each of the project. Are the projects profitable assuming the required rate of return of 10%? Which of them would you choose? The IRR for project A is 14,5%

0 1 -­‐2000 1000 14,49% =irr(b4:f4) 2 800 3 600 4 200

The IRR for project B is 11,8%

0 1 -­‐2000 200 11,79% =irr(b4:f4) 2 600 3 800 4 1200

To find IRR manually, without Excel you need to pick up a starting rate – observe that for rate of 10% project A a positive NPV. This means that IRR should be larger than 10% (remember IRR is the rate that makes NPV = 0). So let us try 15%. NPV at rate of 15% is NPV = -­‐2000 + 1000 / 1.15 + 800 / 1.15^2 + 600 / 1.15^3 + 200 / 1.15^4 = -­‐16.65 Observe that NPV is negative so this means that the IRR we are looking for should be smaller than 15% but the NPV is quite low so it should not be very far away from 15%. So try the rate of 14%: NPV = -­‐2000 + 1000 / 1.14 + 800 / 1.14^2 + 600 / 1.14^3 + 200 / 1.14^4 = +16.16 Now we get a positive NPV so IRR should be larger than 14% but again NPV is quite small, so the logic will be to try 14.5% NPV = -­‐2000 + 1000 / 1.145 + 800 / 1.145^2 + 600 / 1.145^3 + 200 / 1.145^4 = -­‐0.36 Observe that now we have the NPV almost zero so we can say that IRR for project A is equal to 14.5%. Problem 6. You are saving for a new car and have calculated that you will be able to make five payments before you need to buy the car. Your stock market account is expected to earn 8% each year, and you will need \$45,000 to buy the car you want. How much must you save each year to buy the car at the end of five years for the price of the above mentioned \$45,000? Solution

Both projects are profitable since the IRR is higher then the required rate of return. Both of them could be accepted. If we have to choose only one project we should choose project A since it generates the higher IRR.

Solving we get the annual contribution to the account is 7,670.54 Problem 7. Along with your new car in five years, you have decided to buy a new house now. Current mortgage rates are 4% per month, and you have decided to finance the house for 30 years. The house you want is \$860,000, and you are able to finance 80% of that. How much will your payment be?

math

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