Question

TVM: 1. You are interested in saving money for your first house. Your plan is to make regular deposits into a brokerage account that will earn 14 percent. Your first deposit of $5,000 will be made today. You also plan to make four additional deposits at the beginning of each of the next four years. Your plan is to increase your deposits by 10 percent a year. (That is, you plan to deposit $5,500 at t = 1, and $6,050 at t = 2, etc.) How much money will be in your account after five years?

2. Foster Industries has a project that has the following cash flows: Year Cash Flow 0 - $300.00 1 100.00 2 125.43 3 90.12 4 ? What cash flow will the project have to generate in the fourth year in order for the project to have a 15 percent rate of return?

3. John Keene recently invested $2,566.70 in a project that is promising to return 12 percent per year. The cash flows are expected to be as follows: End of Year Cash Flow 1 $325 2 400 3 550 4 ? 5 750 6 800 What is the cash f low at the end of the 4th year?

4. You recently purchased a 20 - year investment that pays you $100 at t = 1, $500 at t = 2, $750 at t = 3, and some fixed cash flow, X, at the end of each of the remaining 17 years. You purchased the investment for $5,544. 87. Alternative investments of equal risk have a required return of 9 percent. What is the annual cash flow received at the end of each of the final 17 years, that is, what is X?

5. Find the present value of an income stream that has a negative flow of $100 per year for 3 years, a positive flow of $200 in the 4th year, and a positive flow of $300 per year in Years 5 through 8. The appropriate discount rate is 4 percent for each of the first 3 years and 5 percent for each of the later years. Thus, a ca sh flow accruing in Year 8 should be discounted at 5 percent for some years and 4 percent in other years. All payments occur at year - end.

Please provide a step by step breadkdown, not just a final answer so I can fully understand this :)

Answer 1

Solution 1)

FV of a growing annuity = P*((1+r)^n-(1+g)^n)/(r-g), P is the amount of first payment, r is interest rate, g is growth rate, n is number of time period

Since this annuity is starting at time 0

Money in account after five years = FV of annuity due = (P*((1+r)^n-(1+g)^n)/(r-g))*(1+r)

Money in account after five years = (5000*((1+15%)^5-(1+10%)^5)/(15%-10%))*(1+15%) = $46,097.43

Solution 2)

CF0 = -300, CF1 = 100, CF2 = 125.43, CF3 = 90.12, CF4 = ?

Required rate of return = 15%

-300 + 100/(1+15%) + 125.43/(1+15%)^2 + 90.12/(1+15%)^3 + CF4/(1+15%)^4 = 0

-58.94502 + CF4/(1.15^4) = 0

CF4 = 58.94502 * (1.15^4) = 103.10

Solution 3)

CF0 = -2566.70, CF1 = 325, CF2 = 400, CF3 = 550, CF4 = ?, CF5 = 750, CF6 = 800

Required Rate of Return = 12%

-2566.7 + 325/(1+12%) + 400/(1+12%)^2 + 550/(1+12%)^3 + CF4/(1+12%)^4 + 750/(1+12%)^5 + 800/(1+12%)^6=0

-735.29 + CF4/(1+12%)^4 = 0

CF4 = 735.29*(1+12%)^4 = 1156.99 or 1157

Solution 4)

CF0 = -5544.87, CF1 = 100, CF2 = 500, CF3 = 750, CF4 to CF20 = X

Required rate of Return = 0

-5544.87 + 100/(1+9%) + 500/(1+9%)^2 + 750/(1+9%)^3 + X*((1-(1+9%)^-17)/9%)*(1+9%)^-3 = 0

-4453.15 + X*6.597251 = 0

X = 4453.15/6.597251 = 675

Solution 5)

CF1 to CF3 = -100, CF4 = 200, CF5 to CF8 = 300 per year in Years 5 through 8.

Discount rate = 4 percent year 1 to 3

Discount Rate = 5 for year 5 to 8

PV of CF1 to CF3 = -100*((1-(1+4%)^-3)/4%) = -277.51 (PV of annuity)

PF of CF4 = 200/(((1+4%)^3)*(1+5%)) = 169.33 (PV discounting at 4% for 3 years & 5% for 1 year)

PV of CF5 = 300/(((1+4%)^3)*(1+5%)^2)

PV of CF6 = 300/(((1+4%)^3)*(1+5%)^3)

PV of CF7 = 300/(((1+4%)^3)*(1+5%)^4)

PV of CF8 = 300/(((1+4%)^3)*(1+5%)^5)

Adding PV of CF5 to CF8 and taking the common factor out,

PV of CF 5 to CF8 = (300/(((1+4%)^3)*(1+5%)^2))*(1+1/(1+5%)+1/(1+5%)^2+1/(1+5%)^3) = 900.67

PV of Income Stream = -277.51 + 169.33 + 900.67 = 792.49