CH08c HW – Even More Time Value

I’m trying to learn for my Business class and I’m stuck. Can you help?

Important General Instructions for Reporting Numerical Answers:

– Do not round intermediate calculations.

-Unless otherwise instructed, round your final answer to 2 decimal places, e.g., “32.16”.

– Unless otherwise instructed, solve problems in the given units. IE: if given units are in $K, complete your computations in these units and, as applicable, report your answer in these units (without writing “$” or “K”).

– Do not report any numerical answer as a percent. IE: for example, write

0.324 instead of 32.4%.

– Report negative numbers with a leading minus sign, like this (for example):

-23.451

Not like this: (23.451).

– Note that Canvas removes trailing insignificant figures. If you type, for example, 41.350, Canvas will remove the last decimal place and record your answer as 41.35 This is fine because 41.35 = 41.350.

– Assume time is measured in years unless otherwise stated.

Q1:

Calculate the effective rate(EAR) assuming an APR of 9 percent compounded quarterly.

(Do not round intermediate calculations and do not enter your answer as a percent. Round your answer to 3 decimal places, e.g., 0.315 instead of 31.5%.)

Q2:

An investment will pay you $80,000 in 10 years. If the APR is 9 percent compounded daily, what is the present value?

Q3:

Elliott Credit Corp. wants to earn an effective annual return (EAR or EAIR) on its consumer loans of 17.1 percent per year. The bank uses daily compounding on its loans. What interest rate is the bank required by law to report to potential borrowers? Hint: The bank is required to report the APR for these loans. (Do not round intermediate calculations and do not enter your answer as a percent. Round your answer to 3 decimal places, e.g., 0.315 instead of 31.5%.)

Q4:

What is the future value of $3,100 in 17 years assuming an APR of 8.4% compounded semi-annually? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Q5:

The appropriate APR for the following cash flows is 9 percent compounded quarterly.

Year

Cash Flow

1

$

815

2

990

3

0

4

1,520

What is the present value of the cash flows? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Q6:

You want to buy a new sports coupe for $84,500, and the finance office at the dealership has quoted you an APR of 5.2 percent compounded monthly for a 60-month loan to buy the car. What will your monthly payments be? (Do not round intermediate calculations and do not enter your answer as a percent. Round your answer to 2 decimal places, e.g., 32.16.)

Q7:

You are planning to make monthly deposits of $475 into a retirement account with an APR of 10 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be just after two months (just after your second deposit)? Round your answer to the nearest dollar.

Q8:

You’ve just joined the investment banking firm of Dewey, Cheatum, and Howe. They’ve offered you two different salary arrangements. You can have a) $85,000 per year for the next two years, or you can have b) $74,000 per year for the next two years, along with a $20,000 signing bonus today. The bonus is paid immediately, and the salary is paid in equal amounts at the end of each month. If the appropriate APR is 7 percent compounded monthly, what is the PV for option b)?

Q9:

You are planning to make Quarterly deposits of $1,000 into a savings account with an APR of 5% interest compounded monthly. Your first deposit will be made one quarter from now, and you want to know what the value of the account will be just after 3 quarters from now. Is the below Cash Flow Diagram appropriate to represent this problem from your perspective?

HW8C_Q10.jpg

A. YES

B. NO

Q10:

Beginning three months from now (one Q from now), you want to withdraw $2,500 each quarter from your bank account to cover college expenses over the next four years. If the account pays r of 0.57% interest per quarter, how much do you need to have in your bank account today to meet your expense needs over the next four years? (Do not round intermediate calculations and do not enter your answers as a percent. Round your answer to 2 decimal places)

Q11:

You plan to make the following deposits into your 4% interest savings account (IE: r = 4%, compounded annually). If you have nothing in your account now and you never make a withdrawal, how much will be in your account when T = 4.5 years?

T (years) Deposit
1.5 200
2 80
3.5 40
5.5 10

Q12:

Find X for “The APR of this investment is X compounded semi-annually,” if the associated EAIR (EAR) is 11.1 percent.

Hint: Note that r in this case = APR/2. Plug APR/2 into the EAIR equation. Solve for APR, then X = APR.

(Do not round intermediate calculations and do not enter your answer as a percent. Round your answer to 3 decimal places, e.g., 0.315 instead of 31.5%.)

Q13:

An investment offers $4,350 per year for forever, with the first payment occurring one year from now.

What is the best way to describe this investment?

A. A perpetual sovereign bond
B. A growing perpetuity
C. An annuity
D. A growing annuity due
E. A growing annuity
F. An annuity due
G. A perpetuity
H. A perpetual annuity due

Q14:

First National Bank (bank a) charges an APR of 13.1 percent compounded monthly on its business loans. First United Bank (bank b) charges an APR of 13.3 percent compounded semiannually.

As a potential borrower, which bank would you go to for a new loan?

A. First United Bank (b)
B. First National Bank (a)

The remaining questions are all about bonds that pay half of their coupons every 6 months.

Q15:

Facebook has just issued its first bond. It’s a 10 year issue with $1,000 face value and a 4% coupon rate. What is the r for this bond?

Hint, r is in time units of 6 months, with semi-annual compounding.

(Do not round intermediate calculations and do not enter your answer as a percent. Round your answer to 3 decimal places, e.g., 0.315 instead of 31.5%.)

Q16:

Facebook issued its first bond on 1/1/20X1. The bond has $1,000 face value, a 4% coupon rate, and it matures on 1/1/20X9. Today, 1/2/20X7, the bond is trading at $1,050 per bond. Which table best represents the remaining contractual Cash Flows for this bond?

A.
Date Cash Flow
1/1/20X8 $40
1/1/20X9 $40
1/1/20X9 $1,000
B.
Date Cash Flow
7/1/20X7 $40
1/1/20X8 $40
7/1/20X8 $40
1/1/20X9 $40
1/1/20X9 $1,050
C.
Date Cash Flow
7/1/20X7 $20
1/1/20X8 $20
7/1/20X8 $20
1/1/20X9 $20
1/1/20X9 $1,000
D.
Date Cash Flow
1/1/20X8 $40
1/1/20X9 $40
1/1/20X9 $1,040

Q18:

Google issued a bond on 1/1/20X1. The bond has $1,000 face value, a 8% coupon rate, and it matures on 1/1/20X9. Today, 1/2/20X7, the bond is trading at $990 per bond. The remaining contractual cash flows for this bond are as listed below.

Date Cash Flow
7/1/20X7 $40
1/1/20X8 $40
7/1/20X8 $40
1/1/20X9 $40
1/1/20X9 $1,000

Which is closest to the r for this bond today?
Hints: r is in time units of 6 months, with semi-annual compounding. Use trial and error. Plug in the suggested r’s until you find the one that works best.

A. 0.043
B. 0.036
C. 0.040
D. 0.049

Q19

Google issued a bond on 1/1/20X1. The bond has $1,000 face value, a 8% coupon rate, and it matures on 1/1/20X9. Today, 1/2/20X7, the bond is trading at $990 per bond. The remaining contractual cash flows for this bond are as listed below.

Date Cash Flow
7/1/20X7 $40
1/1/20X8 $40
7/1/20X8 $40
1/1/20X9 $40
1/1/20X9 $1,000

What is the Yield to Maturity (YTM) of this bond today?
Hints: Start with your answer from the previous Google bond question. Remember YTM = EAIR.

(Do not round intermediate calculations and do not enter your answer as a percent. Round your answer to 3 decimal places, e.g., 0.315 instead of 31.5%.)