Time value of money problems with solutions

FIN 701, PRACTICAL APPLICATION 1, SPRING 2020 AP1

Assume that you are nearing graduation and that you have applied for a job with a local bank. As part of the bank’s evaluation process, you have been asked to take an examination that covers several financial analysis techniques. The first section of the test addresses time value of money analysis. See how you would do by answering the following questions:

For each problem, you need to show your work in order to receive credit. A correct answer with no work shown gets half credit (which means you fail the assignment). An incorrect answer with no work receives 0 credit. With time value of money (TVM) problems, that means showing your inputs for the financial calculator. Make your final answer very clear for the graders. Please don’t make them hunt for your answer.

For example, on 1a, I would show:

N = 3; I/Y = 12; PV = -850; PMT = 0, Calc FV = _______

For uneven cash flows, show CF0 = xx, CF1 = xx F01 = x; CF2 = xx F02 = x, etc.

Show all dollar and percentage values to two decimals ($xxx.xx) and percentage values to x.xx% (be sure to have sufficient decimals showing on your calculator). Rounded answers will receive point deductions.

In some cases, an equation will be easier than using the TVM keys, show your equation if that is the case.

If you use Excel, show what the equation and inputs used.

As with all TVM problems, assume annual compounding unless otherwise specified. Further, assume “regular” annuities (end of period payments) unless specified as “annuities due” (beginning of period payments).

1. (a) If you deposit $200 in the bank today, what is its future value at the end of three years if it is invested in an account paying 12% annual interest, assuming annual compounding? (1 point)

(b) What is the present value of $200 to be received in three years if the appropriate interest rate is 12% (annual compounding)? (1 point)

2. We sometimes need to find how long it will take a sum of money (or anything else) to grow to some specified amount. (a) For example, if a company’s sales are growing at a rate of 18% per year, approximately how long will it take sales to triple? (1 point)

(b) If you want an investment to double in 3 years, what interest rate must it earn? (1 point)

3. (a) What is the difference between an ordinary annuity and an annuity due? (2 points)

(b) What type of annuity is shown in the following cash flow timeline? (1 point)

(c) How would you change it to the other type of annuity? (Think about the cash flows) (1 point)

4. (a) What is the future value of a 3-year ordinary annuity (recall that ordinary annuities have end of year cash flows) of $200 if the appropriate interest rate is 12%? (1 point)

(b) What is the present value of the annuity? (1 point)

(c) What would the future and present values be if the annuity were an annuity due (beginning of year cash flows)? Hint, set your calculator to BGN, there is a video in M2 that shows you how to do this. Don’t forget to reset to “END” after you work an annuity due problem.

(1 pt) PV =

(1 pt) FV =

Note: Look at the difference between an annuity vs. annuity due for the respective PVs and FVs. This relationship is something you will want to remember.

5. What is the present value of the following uneven cash flow stream? The appropriate interest rate is 12%, compounded annually. Note that the final cash flow represents a project where there may be reclamation or other “end of project” costs which are greater than any final income and/or salvage value. (1 point)

6. What annual interest rate will cause $200 to grow to $251.94 in 3 years? (1 point)

7. (a) Will the future value be larger or smaller if we compound an initial amount more often than annually—for example, every 6 months, or semiannually — holding the stated interest rate constant? Explain your answer. (2 points)

(b-1) What is the future value of $200 after three years under 12% semiannual compounding? (1 point)

(b-2) What is the effective annual rate for 12% interest with semiannual compounding? Be sure to show your EAR answer to 2 decimals, that is xx.xx% (1 point)

Hint: Go to practice problem 26 and review the problem and solution. Also note in Moodle: “Video, how to work Practice Problems #26 & 27). This provides a “click by click” solution for EAR problems using the BAII plus with the equation.

· There are multiple ways to calculate EAR, whichever method you use, you need to show your inputs. If using equation: EAR = ( 1 + APR/m)^m, identify APR and m

· If using the financial calculator’s “ICONV” function, identify NOM, and C/Y

· If using Excel’s “effect” function, identify your inputs and how the equation would look in Excel.

(c-1) What is the future value of $200 after three years under 12% quarterly compounding? (1 point)

(c-2) What is the effective annual rate (EAR) for 12% interest with quarterly compounding? (1 point)

(d-1) What is the future value of $200 after three years under 12% daily compounding? Assume 365 day years and do not do any interim rounding. Just enter the interest rate, divide by 365, hit “=”, then hit your I/Y key (or similar for other calculators). (1 point)

(d-2) What is the effective annual rate for 12% interest with daily compounding? (1 point)

8. Will the effective annual rate ever be equal to the simple (quoted) rate? Explain. (1 point)

9. (a) Assume that you have borrowed $1,000 for 2 years and you have an annual interest rate of 12% (annually compounded). What is the monthly payment due on the loan? (1 point)

(b) Switch gears here and now assume that the payments are made annually. What is the annual interest expense for the borrower, and the annual interest income for the lender, during Year 1? (Hint: Go to the TVM lecture notes for multiple cash flows and go to slide 15.) (1 point)

10. Suppose on January 1 you deposit $200 in an account that pays a quoted interest rate of 11.33% (APR), with interest added (compounded) daily. How much will you have in your account on October 1, or after 9 months? (assume N = 273 days) Recall that the interest rate (I/Y) represents the periodic rate based on how many times per YEAR the interest is compounded. Hint, this is 365 times per year. (1 point)

11. Now suppose you leave your money in the bank for 21 months. Thus, on January 1 you deposit $200 in an account that pays a 11.33% compounded daily. How much will be in your account on October 1 of the following year? (assume N = 638 days) (1 point)

12. Suppose someone offered to sell you a note that calls for a $1,000 payment three years from today. The person offers to sell the note for $850. You have $850 in a bank time deposit (savings instrument) that pays a 6.77% APR with daily compounding; and you plan to leave this money in the bank unless you buy the note. The note is not risky—that is, you are sure it will be paid on schedule. Should you buy the note? Check the decision in two ways:

(a) by comparing your future value (FV) if you buy the note versus leaving your money in the bank (FV of the note is $1000, compare this to the FV of leaving $850 in the bank for 3 years with daily interest compounding, should you buy the note?) (1 point)

(b) by comparing the present value (PV) of the note with your current bank investment (PV of the note is PV of the $1000 payout in 3 years assuming the same daily compounded interest as your bank is paying and the PV of your bank investment is the $850, should you buy the note?) (1 point)

(c) Based on parts (a) and (b), do you buy the note or keep your money in the bank? Be sure to explain your answer. (1 point)