# Introduction To Finance Midterm Exam

Quiz #2

This Quiz counts for 15% of the course grade. Make sure you SHOW ALL WORK and LABEL IT CLEARLY. You MUST provide financial calculator inputs AND the answer. Answer-Only responses, even if correct, WILL NOT receive full credit.

Part 1 (12 points) __________

1. If we know the amount for which a coin was purchased thirty (30) years ago, and the annual rate at which its value has grown, finding the VALUE TODAY is a:

a. Future Value (FV) calculation

b. Present Value (PV) calculation

c. Annuity Calculation (because the growth rate remains constant for each of the fifty years)

d. A Perpetuity (because the present value of any sum fifty years out has VERY LITTLE PV)

2. Monthly principal and interest payments under a loan contract with a fixed interest rate and under which the loan will be paid down to $0 after the last payment; with payments beginning ONE MONTH AFTER the borrower gets the Loan Proceeds are in the form of:

a. A Perpetuity

b. A Consol

c. An Annuity DUE

d. An ORDINARY Annuity

3. The button on the TVM row on a financial calculator which is NOT USED in a simple lump sum FUTURE VALUE problem is:

a. the Present Value (PV) key b. the Future Value (FV) key c. the Interest Rate (I/Y) key d. the Payment (PMT) key e. the Number of Periods (N) key

4. Which one of the following will increase the PRESENT VALUE of a lump sum future amount? Assume the interest rate is a positive value and all interest is reinvested.

a. increase in the time period

b. increase in the rate of return

c. decrease in the future value

d. decrease in the rate of return

5. Which of the following statements is TRUE?

a. In an annuity due there is one less “interest” period than in an ordinary annuity

b. For the same stream of Cash Flows (CFs), the future value of an annuity due is GREATER THAN the future value of an ordinary annuity.

c. The “default assumption” with annuity CFs is that they take the form of an annuity due.

6. Which one of the following statements is correct?

a. The present value of an annuity increases when the interest rate increases. b. The present value of an annuity is unaffected by the number of the annuity payments. c. The future value of an annuity is unaffected by the amount of each annuity payment. d. The present value of an annuity increases when the interest rate decreases.

7. The future value of a series of Cash Flows over time can be computed by:

a. computing the future value of the average cash flow and multiplying that amount by the number of cash flows. b. summing the amount of each of the individual cash flows and multiplying the summation by (1 + r)t, where t equals the total number of cash flows. c. summing the future values of each of the individual cash flows. d. discounting each of the individual cash flows and summing the results.

8. ( TRUE or FALSE ) In a “pure discount” Loan, the borrower receives the full amount of the Loan Note at origination, and makes monthly payments until all principal and accrued interest is paid full.

9. ( TRUE or FALSE ) The relationship between Present Value (PV) and Future Value (FV) interest (return) factors is RECIPROCAL.

10. ( TRUE or FALSE ) The foundation of the TVM principle of financial management is the assumption that INFLATION makes future funds less valuable than present funds.

11. ( TRUE or FALSE ) The Rule of 72 provides a means to estimate how long it will take for the value of an asset or investment to DOUBLE.

12. The three potential sources of funding for a company’s assets are BORROWING (Debt), CAPITAL CONTRIBUTIONS (Sale of Stock) and ___Earnings/Profits___________.

Part 2 (38 points) _______________

A. You are considering an investment which will produce Cash Flows of $ 100,000 in Year 1; $ 350,000 in Year 2 and $ 500,000 in Year 3. What is the maximum amount you should pay for this investment is the appropriate annual risk factor is 8%, compounded annually? (6)

(Table A.2)(100,000 x .9259) + (.8573 x 350,000) + (.7938 x 500,000)

92,590 + 300,055 + 396,900 = 789,545

OR: CF0 =0; CF1 = 100,000; CF2 = 350,000; CF3 = 500,000 (ALL F=1); I = 8;

NPV = 789,577

B. You believe you will need $450,000 in supplemental retirement funds 20 years from TODAY. How much must you deposit annually into a fund which is projected to return 5% annually, if the first deposit is made ONE YEAR FROM TODAY? (4)

FVA = PMT (FVIFA, 5%,20) (Table A.4)

450,000 = PMT (33.066) = 13,609.15

OR PV = 0; FV = 450,000; I = 5; N = 20; CPT PMT = 13,609.16

(3) What is the required annual deposit if the first one happens TODAY? (2)

ANS: 450,000/34.719 = 12,961.20 or 13,609.16/1.05 = 12,961.11

C. Your can earn 1% semiannually (6 months) at a local bank If you deposit $10,000 TODAY, HOW LONG (how many months) will it take before your account balance is $ 18,167? (5)

ANS: 60 periods (30 years) (Table A.1, 1%, 60 periods)

PV = -1; FV = 1.8167 I = 1 CPT N = 60 N is 60 semiannual periods or 30 years

D. You are considering buying a Bond which will pay $75 interest annually in PERPETUITY. The appropriate risk factor for this investment decision is 9%. The Bonds is currently selling for $900. Should you buy the Bond? (SHOW ALL CALCULATIONS)(4)

ANS: Value of Perpetuity = C/R = 75/.09 = 833.33 Do not buy the Bond because the PV of the perpetual stream of interest payments is less that the cost

E. You have an insurance settlement of a personal injury claim which will pay you $35,000 equal annual installments for the next 21 years, beginning one year from now. J. G Wentworth has offered to buy the settlement contract from you. You believe the appropriate risk factor for this decision is 9%. What is the SMALLEST amount you should accept from J. G Wentworth?(5)

PV of annuity (Table A.3) PVA = PMT x PVIFA9%,21pds

X = 35,000 x 9.2922 = 325,227

OR PMT = 35,000; N = 21; I = 9; CPT PV = 325,228

F. How much will accumulate at the end of 3 years in an account which earns 10%, compounded semiannually, if deposits are made $110,000 TODAY; $ 145,000 one year from now; and $ 200,000 two years from now? (4) (Table A.1)

ANS: (110,000 x FVIF5%,6pds) + (145,000 FVIF55,4pds) + (200,000 x FVIF5%,2pds) = (110,000 x 1.3401) + (145,000 X 1.2155) + (200,000 x 1.1025)

= 147,411 + 176,247.5 + 220,500 = 544,158.50

What TOTAL DOLLAR AMOUNT OF RETURN was earned on this account? (2)

ANS: 544,158.5 — 455,000 = 89,158.5

G. You have applied for a $ 1,000,000 loan on which a bank will charge 8% interest compounded annually. The loan will be repaid in three EQUAL ANNUAL installments beginning one year after you receive the loan proceeds.

What will the annual installment payment be? (2)

ANS: PV = 1,000,000; FV = 0: I = 8; N =3; CPT PMT = 388,034

Prepare an amortization table showing how loan payments will be applied (down to $0 balance). (4 points)

Beg Interest Total Payment Balance

1,000,000 80,000 1,080,000 388,034 691,966

691,966 55,357 747,323 388,034 359,289

359,289 28,743 388,032 388,034 –0–