Question 1

You want to start a business that you believe can produce cash flows of $5,600, $48,200, and $125,000 at the end of each of the next three years, respectively. At the end of three years you think you can sell the business for $250,000. At a discount rate of 16 percent, what is this business worth today?

Accepted Answer

To calculate the present value of cash flows, we need to use the formula:
PV = CF1 / (1+r)^1 + CF2 / (1+r)^2 + CF3 / (1+r)^3 + Terminal Value / (1+r)^3
Where PV is the present value, CF is the cash flow, r is the discount rate, and Terminal Value is the value of the business at the end of three years.

Plugging in the given values, we get:
PV = 5,600 / (1+0.16)^1 + 48,200 / (1+0.16)^2 + 125,000 / (1+0.16)^3 + 250,000 / (1+0.16)^3
PV = 4,827.586 + 36,614.213 + 71,203.800 + 77,249.065
PV = 189,894.664

Therefore, the business is worth $189,894.67 today, which is closest to option C, $280,894.67.

Question 2

An amortized loan:

Accepted Answer

An amortized loan may have equal or increasing amounts applied to the principal from each loan payment. This means that with each payment, a portion goes towards paying off the principal amount of the loan in addition to the interest. The amount applied to the principal gradually increases over time, leading to a decrease in the amount of interest paid and a quicker repayment of the loan.

Question 3

A proposed project has cash flows of $2,000, $?, $1,750, and $1,250 at the end of Years 1 to 4. The discount rate is 7.2 percent and the present value of the four cash flows is $6,669.25. What is the value of the Year 2 cash flow?

Accepted Answer

The answer of A proposed project has cash flows of...

Question 4

Your grandmother will be gifting you $150 at the end of each month for four years while you attend college. At a discount rate of 3.7 percent, what are these payments worth to you on the day you enter college?

Accepted Answer

To calculate the present value of the payments, we use the formula: 
PV = PMT * [1 - (1 / (1 + r)^n)] / r

Where: 
PV = Present value 
PMT = Payment amount 
r = Discount rate 
n = Number of periods

In this case, PMT = $150, r = 3.7%, and n = 48 (4 years * 12 months).

Plugging these values into the formula:

PV = $150 * [1 - (1 / (1 + 0.037)^48)] / 0.037 
PV = $6,682.99

So the answer is B, $6,682.99.

Question 5

One year ago, JK Mfg. deposited $12,000 in an investment account for the purpose of buying new equipment four years from today. Today, it is adding another $15,000 to this account. The company plans on making a final deposit of $10,000 to the account one year from today. How much cash will be available when the company is ready to buy the equipment assuming an interest rate of 5.5 percent?

Accepted Answer

The answer of One year ago, JK Mfg. deposited $12,000...

Question 6

A charity plans to invest annual payments of $60,000, $70,000, $75,000, and $50,000, respectively, over the next four years. The first payment will be invested one year from today.  Assuming the investment earns 5.5 percent annually, how much will the charity have available four years from now?

Accepted Answer

We can solve this problem by using the formula for the future value of an annuity, which is:

FV = PMT x ((1 + r)n - 1) / r

where PMT is the annual payment, r is the annual interest rate, and n is the number of years.

Plugging in the values given in the problem, we get:

FV = 60,000 x ((1 + 0.055)4 - 1) / 0.055 + 
     70,000 x ((1 + 0.055)3 - 1) / 0.055 + 
     75,000 x ((1 + 0.055)2 - 1) / 0.055 + 
     50,000 x ((1 + 0.055)1 - 1) / 0.055

FV = 60,000 x 4.310108 + 70,000 x 3.310809 + 75,000 x 2.619137 + 50,000 x 1.055

FV = 258,606.48 + 231,758.63 + 196,439.03 + 52,750.00

FV = $739,554.14

Therefore, the charity will have $739,554.14 available four years from now. The closest answer choice to this amount is C) $277,491.

Question 7

The entire repayment of a(n) ________ loan is computed simply by computing one single future value.

Accepted Answer

A pure discount loan is repaid by paying a single lump sum at maturity, which is the future value of the loan amount.

Question 8

Your anticipated wedding is three years from today. You don't know who your spouse will be but you do know that you are saving $10,000 today and $17,000 one year from today for this purpose. You also plan to pay the final $12,000 of anticipated costs on your wedding day. At a discount rate of 5.5 percent, what is the current cost of your upcoming wedding?

Accepted Answer

The current cost of the upcoming wedding can be calculated by discounting the future payments back to their present value using the given discount rate of 5.5 percent. The calculation involves the present value of a single sum formula for each payment:1. $10,000 is already in today's dollars, so it remains $10,000.2. $17,000 one year from today: PV = FV / (1 + r)^n = $17,000 / (1 + 0.055)^1 = $16,107.143. $12,000 three years from today: PV = $12,000 / (1 + 0.055)^3 = $10,225.97Adding these up gives the total current cost: $10,000 + $16,107.14 + $10,225.97 = $36,333.11

Question 9

You are considering a project with cash flows of $16,500, $25,700, and $18,000 at the end of each year for the next three years, respectively. What is the present value of these cash flows, given a discount rate of 7.9 percent?

Accepted Answer

To find the present value of these cash flows, you can use the formula:
PV = CF1 / (1 + r)^1 + CF2 / (1 + r)^2 + CF3 / (1 + r)^3
Plugging in the values, we get:
PV = 16,500 / (1 + 0.079)^1 + 25,700 / (1 + 0.079)^2 + 18,000 / (1 + 0.079)^3
PV = 15,336.71 + 22,052.83 + 14,305.61
PV = 51,695.15
Therefore, the present value of the cash flows is $51,695.15. Choice B is the best choice.

Question 10

Your broker is offering 1.2 percent compounded daily on its money market account. If you deposit $7,500 today, how much will you have in your account 15 years from now?

Accepted Answer

The answer of Your broker is offering 1.2 percent compounded...

Question 11

You need $25,000 today and have decided to take out a loan at 7 percent interest for five years. Which one of the following loans would be the least expensive for you? Assume all loans require monthly payments and that interest is compounded on a monthly basis.

Accepted Answer

An amortized loan with equal principal payments would be the least expensive option because it would result in the lowest total amount of interest paid over the five-year period. The interest-only loan would result in the highest total amount of interest paid, while the amortized loan with equal loan payments and balloon loan would result in higher amounts of interest paid compared to the equal principal payments option. A discount loan is not applicable in this scenario as it typically involves buying a bond at a discount and then receiving the face value at maturity.

Question 12

Southern Tours is considering acquiring Holiday Vacations. Management believes Holiday Vacations can generate cash flows of $218,000, $224,000, and $238,000 over the next three years, respectively. After that time, they feel the business will be worthless. If the desired rate of return is 14.5 percent, what is the maximum Southern Tours should pay today to acquire Holiday Vacations?

Accepted Answer

The correct answer is A. The maximum Southern Tours should pay today to acquire Holiday Vacations is $519,799.59. This is calculated using the present value of the cash flows, which is $519,799.59. The present value is calculated by dividing the future cash flows by the discount factor, which is 1 + the desired rate of return. In this case, the desired rate of return is 14.5 percent, so the discount factor is 1.145.

Question 13

With an interest-only loan the principal is:

Accepted Answer

With an interest-only loan, the borrower only pays interest on the loan during the loan period. The principal is not being paid down during the loan period, so it must be repaid in full at the end of the loan period, usually in one lump sum payment.

Question 14

You just signed a consulting contract that will pay you $38,000, $42,000, and $45,000 annually at the end of the next three years, respectively. What is the present value of this contract given a discount rate of 10.5?

Accepted Answer

The present value of the contract is calculated by discounting each payment back to the present value using the formula PV = FV / (1 + r)^n. Calculating for each year and summing them gives $102,138.76.

Question 15

You are considering two savings options. Both options offer a rate of return of 7.6 percent. The first option is to save $2,500, $2,500, and $3,000 at the end of each year for the next three years, respectively. The other option is to save one lump sum amount today. You want to have the same balance in your savings account at the end of the three years, regardless of the savings method you select. If you select the lump sum method, how much do you need to save today?

Accepted Answer

To find the equivalent lump sum amount that needs to be saved today to have the same balance at the end of three years as the first option, we calculate the future value of each annual saving and then find the present value of the total future value at the given rate of 7.6%. The future value of the savings at the end of three years can be calculated using the formula FV = P * (1 + r)^n, where P is the principal amount, r is the annual interest rate, and n is the number of years. Then, to find the present value of this total future value, we use the formula PV = FV / (1 + r)^n. Calculating the future values of each saving and discounting them back to the present at 7.6% will give us the lump sum amount needed today, which matches option D, $6,890.89.

Question 16

Sue plans to save $4,500, $0, and $5,500 at the end of Years 1 to 3, respectively. What will her investment account be worth at the end of the Year 3 if she earns an annual rate of 4.15 percent?

Accepted Answer

The answer of Sue plans to save $4,500, $0, and...

Question 17

You have some property for sale and have received two offers. The first offer is for $89,500 today in cash. The second offer is the payment of $35,000 today and an additional guaranteed $70,000 two years from today. If the applicable discount rate is 11.5 percent, which offer should you accept and why?

Accepted Answer

To determine which offer is better, we need to find their net present value (NPV) and choose the higher one.

For the first offer, the NPV is simply the cash amount offered:

NPV1 = $89,500

For the second offer, we need to discount the future payment of $70,000 back to present value:

NPV2 = $35,000 + $70,000 / (1 + 0.115)² 
NPV2 = $35,000 + $53,505.70 
NPV2 = $88,505.70

Comparing the two offers, we see that the second offer has a higher NPV, so we should accept it. This means we will receive more cash in today's dollars.

Question 18

Waldo expects to save the following amounts: Year 1 = $50,000; Year 2 = $28,000; Year 3 = $12,000. If he can earn an average annual return of 10.5 percent, how much will he have saved in this account exactly 25 years from the time of the first deposit?

Accepted Answer

The answer of Waldo expects to save the following amounts:...

Question 19

Your parents have made you two offers. The first offer includes annual gifts of $5,000, $6,000, and $8,000 at the end of each of the next three years, respectively. The other offer is the payment of one lump sum amount today. You are trying to decide which offer to accept given the fact that your discount rate is 6.2 percent. What is the minimum amount that you will accept today if you are to select the lump sum offer?

Accepted Answer

The present value of the annuity is $16,707.06. This is the minimum amount that you will accept today if you are to select the lump sum offer.

Question 20

Troy will receive $7,500 at the end of Year 2. At the end of the following two years, he will receive $9,000 and $12,500, respectively. What is the future value of these cash flows at the end of Year 6 if the interest rate is 8 percent?

Accepted Answer

To calculate the future value of the cash flows, we can use the formula:

FV = CF1 x (1 + r)^n-1 + CF2 x (1 + r)^n-2 + CF3 x (1 + r)^n-3 + CF4 x (1 + r)^n-4

Where: 
    CF1 = $0 (since there is no cash flow at the end of Year 1) 
    CF2 = $7,500 
    CF3 = $9,000 
    CF4 = $12,500 
    r = 8% 
    n = 6 (since we want to calculate the future value at the end of Year 6)

Plugging in the values:

FV = $0 x (1 + 0.08)^5 + $7,500 x (1 + 0.08)^4 + $9,000 x (1 + 0.08)^3 + $12,500 x (1 + 0.08)^2 
   = $0 + $9,945 + $9,228 + $12,948 
   = $36,121.08

Therefore, the best choice is C.

Quiz 6: Discounted Cash Flow Valuation