Question

1. You decided to save all of tax refunds next four years. Given your projection of your annual income and effective tax rate, you believe that you will be able to invest $3,000, $3,300, $3,800, and $4,000 next four years, respectively, starting a year from today. Your estimated rate of return on this investment is 5%. How much can you withdraw in 4 years? Round to the nearest cent. (2 decimal)

2. What is the effective annual yield of 6% compounded monthly? Answer in the percent format. Round to the nearest hundredth percent.

3. Atlas is looking at a security that is expected to pay an annual cash flow next year of $4.20 per year . The cash flow is expected to grow by 5 percent annually. If investors require a 16 percent return on similar risk securities, how much is the security worth?

Answer 1

1.

Please note that, i have assumed that for all the years, we are investing the money at the start of the year. So, money invested in year 1 will have 4 periods of compounding, year 2 money will have 3 period of compounding and so on.

Value of money invested in year 1 = 3000 * ( 1.05)^4

Value of money invested in year 2 = 3300 * ( 1.05)^3

Value of money invested in year 3 = 3800 * ( 1.05)^2

Value of money invested in year 4 = 4000 * ( 1.05)^1

You can change your answer, if we assume that money is getting invested at the end of the year

Value of money invested in year 1 = 3000 * ( 1.05)^3

Value of money invested in year 2 = 3300 * ( 1.05)^2

Value of money invested in year 3 = 3800 * ( 1.05)^1

Value of money invested in year 4 = 4000 * ( 1.05)^0

2.)

Annual yeild = 6%

Effective annual yield compounded monthly = ( 1 + yield / 12 ) ^ 12 - 1

Effective annual yield compounded monthly = ( 1 + 0.06 / 12 ) ^ 12 - 1 = 6.168%

3)

Cash flow = 4.20 per year

growth rate = 5%

return = 16%

Price of security = Cash flow * ( 1+ growth rate ) / ( return - growth rate )

This is Gordon growth formula for calculating the value of security

Price of security = 4.20 * ( 1.05 ) / ( 0.16 - 0.05) = $49

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