Question 1

Suzette is going to receive $10,000 today as the result of an insurance settlement. In addition, she will receive $15,000 one year from today and $25,000 two years from today. She plans on saving all of this money and investing it for her retirement. If Suzette can earn an average of 11% on her investments, how much will she have in her account if she retires 25 years from today?

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Question 2

Sue just signed a contract wherein she will receive the following payments. What is the contract worth to her today if she can earn 7% on her investments?

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Question 3

You plan on making monthly payments for the next ten years in order to accumulate $100,000. If the rate of return is 8% compounded monthly, determine the value of the monthly payments.

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Question 4

Johnston Corporation wishes to purchase an apartment complex that provides annual cash flows from rental property of $5,000,000. Rental increase is approximated at 1.5% per year into the foreseeable future. If Johnston's return requirement is 12.5%, determine the value of the apartment complex.

Accepted Answer

The value of the apartment complex is $45.45 million. This is calculated by dividing the annual cash flows of $5,000,000 by the return requirement of 12.5%.

Question 5

You estimate that you will have $32,800 in student loans by the time you graduate. The interest rate is 4.5%. If you want to have this debt paid in full within five years, how much must you pay each month?

Accepted Answer

To calculate the monthly payment for a loan, you can use the loan payment formula or a financial calculator. The formula for the monthly payment on a fixed-rate loan is P = [r*PV] / [1 - (1 + r)^-n], where P is the monthly payment, r is the monthly interest rate (annual rate divided by 12), PV is the present value or initial loan amount, and n is the total number of payments (months). For this problem, the loan amount (PV) is $32,800, the annual interest rate is 4.5% (or 0.045 when expressed as a decimal), and the loan term is 5 years (or 60 months). The monthly interest rate is 0.045 / 12 = 0.00375. Plugging these values into the formula gives a monthly payment of approximately $611.49.

Question 6

You are borrowing money today at an 8% interest rate. You will repay the principle plus all the interest in one lump sum of $6,500 three years from today. How much are you borrowing?

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Question 7

You are comparing two annuities with equal present values. The applicable discount rate is 7.5%. One annuity pays $5,000 on the first day of each year for twenty years. How much does the second annuity pay each year for twenty years if it pays at the end of each year?

Accepted Answer

Since both annuities have equal present values, we can assume that they both have the same value today. We can use the formula for the present value of an annuity to find out what that value is:

PV = PMT * ((1 - (1 / (1 + r)^n)) / r)

Where PV is the present value, PMT is the payment amount, r is the discount rate, and n is the number of periods.

For the first annuity, we know that the present value is equal to the payments multiplied by the present value factor:

PV = $5,000 * ((1 - (1 / (1 + 0.075)^20)) / 0.075)
PV = $52,846.20

Since we know the present value of both annuities is the same, we can use this value to solve for the payment amount of the second annuity:

PV = PMT * ((1 - (1 / (1 + r)^n)) / r)
$52,846.20 = PMT * ((1 - (1 / (1 + 0.075)^20)) / 0.075)
PMT = $5,375.20

Therefore, the second annuity pays $5,375 at the end of each year for twenty years. The best choice is D.

Question 8

You estimate that you will have $24,500 in student loans by the time you graduate. The interest rate is 6.5%. If you want to have this debt paid in full within five years, how much must you pay each month?

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Question 9

The preferred stock of ABC Co. offers an 8.4% rate of return. The stock is currently priced at $50.00 per share. What is the amount of the annual dividend?

Accepted Answer

The annual dividend is calculated by multiplying the rate of return (8.4%) by the price per share ($50.00). Thus, 0.084 * $50.00 = $4.20.

Question 10

What is the future value of the following cash flows at the end of year 3 if the interest rate is 9.75%?

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Question 11

You plan on making quarterly payments for the next ten years in order to accumulate $350,000. If the rate of return is 5% compounded quarterly, determine the value of the quarterly payments.

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Question 12

You are considering a project with the following cash flows:  What is the present value of these cash flows, given a 9% discount rate?

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Question 13

Calculate the present value of a growing annuity given the following information: annual cash flows = $60,000; cash flow growth rate = 2 %; required rate of return = 7%; timeframe = 10 years.

Accepted Answer

The present value of a growing annuity is calculated using the following formula:PV = C * [(1 - (1 + g)^-n) / (r - g)]Where:C = annual cash flowsg = cash flow growth rater = required rate of returnn = timeframePlugging in the given values, we get:PV = 60,000 * [(1 - (1 + 0.02)^-10) / (0.07 - 0.02)]PV = 60,000 * [(1 - 0.8264) / 0.05]PV = 60,000 * [0.1736 / 0.05]PV = 60,000 * 3.472PV = $456,390Therefore, the present value of the growing annuity is $456,390.

Question 14

You are planning to borrow $2,501. You can repay the loan in 40 monthly payments of $79.06 each or 36 monthly payments of $85.93 each. You decide to take the 40 month loan. During each of the first 36 months you make the loan payment and place the difference between the two payments ($6.87) into a savings account earning 14.4% APR. Beginning with the 37^thpayment you will withdraw money from the savings account to make your payments. How much money will remain in the savings account after your loan is repaid?

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Question 15

Kwantlen University received a significant donation of $50,000 per year for the next fifteen years, with the first payment being received today. Given a discount rate of 5.5%, determine the present value of the donation.

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Question 16

The Home Improvement Center (HIC) has an employment contract with the newly hired CEO. The contract requires a lump sum payment of $32.4 million be paid to the CEO upon the successful completion of her first five years of service. HIC wants to set aside an equal amount of money at the end of each year to cover this anticipated cash outflow and will earn 7.25% on the funds. How much must HIC set aside each year for this purpose?

Accepted Answer

To find the amount HIC must set aside each year, we use the formula for the future value of an annuity, which is FV = P * [((1 + r)^n - 1) / r], where FV is the future value ($32.4 million), P is the annual payment, r is the annual interest rate (7.25% or 0.0725), and n is the number of periods (5 years). Rearranging the formula to solve for P gives us P = FV / [((1 + r)^n - 1) / r]. Plugging in the values gives P = $32,400,000 / [((1 + 0.0725)^5 - 1) / 0.0725], which calculates to approximately $5,606,026.

Question 17

A 9% preferred stock pays an annual dividend of $4.50. What is one share of this stock worth today?

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Question 18

You have a 25-year $800,000 mortgage with a 4.5% rate of interest (compounded monthly) that you make monthly payments on. What is the balance of the loan at the end of year 12?

Accepted Answer

The correct answer is A because the balance of the loan at the end of year 12 is $524,450. This can be calculated using the formula for the balance of a loan:B = P * (1 + r/n)^(nt) - (P * r/n) * ((1 + r/n)^(nt) - 1)where:B is the balance of the loanP is the principal amount of the loanr is the annual interest raten is the number of times per year that interest is compoundedt is the number of yearsIn this case, the principal amount of the loan is $800,000, the annual interest rate is 4.5%, interest is compounded monthly (so n = 12), and the number of years is 12. Plugging these values into the formula, we get:B = 800000 * (1 + 0.045/12)^(12*12) - (800000 * 0.045/12) * ((1 + 0.045/12)^(12*12) - 1)B = 800000 * (1.00375)^144 - (800000 * 0.00375) * ((1.00375)^144 - 1)B = 800000 * 1.6528 - (30000) * (1.6528 - 1)B = 1322240 - 45280B = $524,450

Question 19

You are borrowing money today at a 7.5% interest rate. You will repay the principal plus all the interest in one lump sum of $7,500 two years from today. What is the amount of the loan proceeds?

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Question 20

You initially deposit $25,000 and contribute $250 per quarter for the next 10 years. If the rate of interest is 4% compounded quarterly, calculate the future value.

Accepted Answer

The future value of an investment can be calculated using the formula for the future value of an annuity and adding it to the future value of a lump sum. The future value of the lump sum (initial deposit) is calculated using the formula $FV = PV(1 + r)^n$, where $PV$ is the present value, $r$ is the interest rate per period, and $n$ is the number of periods. The future value of the annuity (quarterly contributions) is calculated using the formula $FV_{\text{annuity}} = P\frac{(1 + r)^n - 1}{r}$, where $P$ is the payment per period, $r$ is the interest rate per period, and $n$ is the number of periods.Given:- Initial deposit ($PV$) = $25,000- Quarterly contribution ($P$) = $250- Annual interest rate = 4% or 0.04- Interest rate per quarter = $0.04 / 4 = 0.01$ or 1%- Number of years = 10- Number of quarters ($n$) = $10 \times 4 = 40$First, calculate the future value of the initial deposit:$$FV_{\text{lump sum}} = 25000(1 + 0.01)^{40}$$Then, calculate the future value of the quarterly contributions:$$FV_{\text{annuity}} = 250\frac{(1 + 0.01)^{40} - 1}{0.01}$$Adding both values gives the total future value of the investment. When you perform these calculations, you should find that the total future value closely matches option A, $49,443. This accounts for both the compounded interest on the initial deposit and the compounded interest on the quarterly contributions.

Quiz 6: Discounted Cash Flow Valuation