QBank Questions: Course 101 Ch. 6

Philip purchased a house for $185,000 with a down payment of 20%. How much is his monthly payment if he finances the balance of the mortgage at 10% over 15 years? A) $1,590.42. B) $1,988.02. C) $1,971.59. D) $1,577.27.

A. n = 180 i = 0.8333 (10 ÷ 12) PV = $148,000 PMToa = ($1,590.42) QB.101.6

Tom and Mary Jane want to purchase a beach house 5 years from today. They know they will have to accumulate at least $150,000 in today's dollars. They expect to earn a 10% after-tax rate of return (compounded annually) and anticipate an average annual inflation rate of 4%. They want to make equal payments, adjusted for inflation, at the end of each year. What serial payments will they have to make at the end of years 2 and 5, respectively? (Round to the nearest dollar) A) $28,914 and $32,524. B) $26,732 and $27,801. C) $30,070 and $31,273. D) $27,801 and $28,913.

A. (END mode) FV = $150,000 PV = 0 i = 5.7692 [((1.10 ÷ 1.04) − 1) × 100] n = 5 PMT = ($26,732.35) $26,732.35 × 1.04 = $27,801.64 = Payment at end of year 1 Payment at end of year 2 = $27,801.64 × 1.04 = $28,913.71 Payment at end of year 3 = $28,913.71 × 1.04 = $30,070.26 Payment at end of year 4 = $30,070.26 × 1.04 = $31,273.07 Payment at end of year 5 = $31,273.07 × 1.04 = $32,523.99 QB.101.6

If the net present value of a series of discounted cash flows is less than zero, one could interpret that: 1. The discounted cash flows are lower than the investment outlay. 2. The rate of return is higher than the cost of capital. 3. The return on investment is higher than the internal rate of return. 4. The internal rate of return equals the discount rate. A) 1 only. B) 2 only. C) 1 and 4 D) 2 and 3.

A. A negative net present value of a series of discounted cash flows means the investment outlay exceeds the discounted cash flows. Net present value is the difference between the initial cash flows and the present value of future cash inflows. If the net present value is negative, the present value of future cash flows is less than the initial investment. An investment with a negative net present value is generally an undesirable investment. QB.101.6

Margaret has just retired. She has a retirement account of $500,000, and she anticipates making an annual withdrawal from the account at the beginning of each year for 30 years. She expects to earn an annual rate of return of 6% on the account. If she adopts a capital utilization (annuitization) approach to her account, how much will she withdraw from the account at the beginning of each year? A) $34,268. B) $36,324. C) $16,667. D) $30,000.

A. Margaret is using a capital utilization approach, which means she intends to completely deplete the balance of the account during her 30 years of retirement. Therefore, the amount she will withdraw each year is $34,268, calculated as follows: (In BEG Mode) $500,000 ± PV $0 FV 30 N 6 I/YR Solve for PMT = $34,268 QB.101.6

Shirley and Leslie, both in their 50s, are finalizing their retirement plan with their financial planner. Their financial planner is reviewing the two most common methods of utilizing their assets during retirement. Which of the following statements regarding these retirement funding methods is(are) correct? 1. Capital retention is the method whereby all funds are depleted over a given period 2. Capital utilization is the method that uses interest only to make the necessary payments A) Neither I nor II B) I only C) Both I and II D) II only

A. Neither statement I nor II is correct. There are two broad methods of computing any form of needs (retirement) analysis: (1) capital utilization (or annuitization), whereby all funds are depleted over a given period; and (2) capital retention (or capital preservation), which uses interest only to make the necessary payments. QB.101.6

Which of the following statements concerning discounted cash-flow analysis techniques is (are) CORRECT? 1. If the result of a net present value calculation is negative, that is, if the present value of the inflow stream is less than the present value of the outflow stream, the investment should be considered. 2. A positive net present value means that the rate of return provided by the investment exceeds the discount rate being used as the benchmark. A) II only. B) Both I and II. C) I only. D) Neither I nor II.

A. Statement I is incorrect because if the result of a net present value calculation is positive, that is, if the present value of the inflow stream exceeds the present value of the outflow stream, the investment is a sound choice. QB.101.6

Robert plans to retire in 10 years. When he retires, he wants to withdraw $50,000 from his retirement account each year, and his objective is to ensure that the balance in the account when he dies is the same as it was at the beginning of his retirement. Which of the following statements regarding Robert's approach is (are) CORRECT? 1. Robert is practicing a capital retention approach. 2. Robert is practicing a capital utilization (annuitization) approach. 3. Robert will need a larger retirement account to accomplish his objective than he would need if he planned to deplete the account balance during his retirement. A) 1 and 3. B) 2 and 3. C) 2 only. D) 1 only.

A. Statements 1 and 3 are correct. Robert is practicing a capital retention approach because he plans to retain the original capital in his account for the duration of his retirement. He will need a larger account balance to accomplish his objective than he would need if he planned to deplete his account (using the capital utilization or annuitization approach) because he will be using only the interest on the account. QB.101.6

What is the net present value of the following cash flows made at the end of the year earning 5% compounded annually? Year 1: $400 Year 2: $100 Year 3: $300 A) $731. B) $762. C) $767. D) $757.

A. The net present value of these cash flows is $731. Keystrokes on the HP10BII are as follows: Uneven cash flow method CF0 = $0 CF1 = $400 CF2 = $100 CF3 = $300 I/YR = 5 NPV = $731 QB.101.6

An investor owns a municipal bond with a coupon rate of 4.5%. The investor's federal marginal income tax rate is 28%. What is the taxable equivalent yield? A) 6.25%. B) 5.76%. C) 3.24%. D) 3.52%.

A. The taxable equivalent yield on this bond is 6.25%, calculated as follows: 4.5% ÷ (1 − 0.28) = 4.5% ÷ 0.72 = 6.25% QB.101.6

Assume Dan can invest in real estate cash flows that will return $1,000 at the end of each year for 20 years after expenses. There is no residual value at the end of the 20 years. How much will Dan be willing to pay for the cash flows, if an annual rate of return of 10% is desired? A) $6,623. B) $8,513. C) $7,456. D) $7,899.

B. This a present value of an annuity calculation. The annuity is $1,000 per year, the number of compounding periods is 20, and the interest rate is 10%. (END mode) FV = $0 PMT = $1,000 i = 10 n = 20 PV = $8,513.56 OR CFj = $0 CFj = $1,000 Nj = 20 I/YR = 10 shift NPV = $8,513.56 QB.101.6

Jane has an opportunity to buy her uncle's business at the end of 5 years. The purchase will require a down payment in 5 years of $200,000 in today's dollars. Assuming a 3% inflation rate and a 10% annual after-tax rate of return on her investments, what serial payment will Jane have to make at the end of years 1 and 2, respectively to fund her goal? A) $34,920.00 and $35,479.28. B) $35,967.52 and $37,046.55. C) $35,479.28 and $35,967.60. D) $37,046.63 and $38,158.03.

B. Solve for the payment due at the end of years 1 and 2, assuming a 3% inflation rate and a 10% after-tax rate of return. The calculation is as follows: (END mode) FV = $200,000 PV = $0 i = 6.796 [((1.10 ÷ 1.03) − 1) × 100] n = 5 PMT = ($34,919.92) Because the payment is at the end of the year, adjust the payments for inflation. PMT1 = $34,919.92 × 1.03 = $35,967.52 PMT2 = $35,967.52 × 1.03 = $37,046.55 QB.101.6

Suppose John and Joan purchased a $175,000 house, paying $20,000 in cash as a down payment and obtaining a 10%, 15-year mortgage for $155,000. Calculate their monthly payment. A) $1,652. B) $1,666. C) $1,360. D) $1,809.

B. The loan amount is $155,000, the number of compounding periods is 180, and the interest rate is 10%. (END mode) PV = ($155,000) FV = 0 i = 0.8333 (10 ÷ 12) n = 180 (15 × 12) PMT = $1,665.64 QB.101.6

Larry has the opportunity to purchase an office building that will provide an expected net operating income of $10,000 per year at the end of each year for 7 years. He believes he can sell the property for $185,000 net of expenses at the end of seven years. If Larry's required rate of return is 15% and the property cost $100,000, what is the NPV of the investment? A) $14,823. B) $11,153. C) $10,567. D) $8,904.

B. The net present value of these cash flows is $11,153. Keystrokes on the HP10BII are as follows: Uneven cash flow method 100000 ± CFj 10000 CFj 6 shift Nj 195000 CFj (185,000 + 10,000) 15 I/YR shift NPV $11,152.5497 QB.101.6

John's estimated real estate investment cash flows at the beginning of each year, starting today, for the next six years are as follows: Year 1: ($12,000) Year 2: ($13,000) Year 3: $14,000 Year 4: $6,000 Year 5: $8,000 Year 6: $9,000 Using a discount rate of 10%, what is the net present value? A) $23,818. B) $3,312. C) $29,874. D) $27,130.

B. The net present value of these cash flows is $3,312.35. Uneven cash flow method CF0 = ($12,000) CF1 = ($13,000) CF2 = $14,000 CF3 = $6,000 CF4 = $8,000 CF5 = $9,000 I/YR = 10 NPV = $3,312.35 QB.101.6

Allen's mortgage is $120,000 for 15 years and has an interest rate of 7%. He makes monthly payments. What is the total amount of interest he will pay over the term of the mortgage? (Select the closest answer.) A) $90,000. B) $80,000. C) $75,000. D) $85,000.

C. PV = $120,000 n = 180 i = 0.5833 (7 ÷ 12) PMTOA = ($1,078.59) × 180 = $194,146.90 − $120,000 = $74,146.90 When calculating this problem, you will need to change the sign of $194,146.90 to positive before subtracting $120,000. QB.101.6

Brian, age 48, plans to retire at 65 and wants to be debt free at retirement. The mortgage balance shown on his statement of financial position is $114,042 at the end of the 10th year of a 30-year loan. The monthly payment from the statement of cash flows (principal and interest only) was $953.89. What was the original balance of the loan if the interest rate was 8%? A) $125,000. B) $119,572. C) $130,000. D) $140,428.

C. n = 360 (30 × 12) i = 0.6667 (8 ÷ 12) PMTOA = $953.89 FV = $0 PV = $130,000 QB.101.6

Troy and Samantha would like to plan for their daughter's college education. They would like their daughter, who was born today, to attend a public university for 4 years beginning at age 18. Tuition is currently $15,000 a year and has increased at an annual rate of 6%, while inflation has only increased at 2.5% per year. They can earn an investment rate of return of 9%. How much must they save at the end of each year if they would like to make the last payment at the beginning of their daughter's first year of college? (Round to the nearest dollar) A) $3,650 B) $2,945 C) $3,979 D) $4,236

C. Keystrokes on the HP10BII are as follows: Uneven Cash Flow Method Step 1: Determine the PV of the years of tuition at age 18. 0 CFj 0 CFj 17 Shift Nj 15000 CFj 4 Shift Nj [(1.09 ÷ 1.06) − 1] × 100 = 2.8302 I/YR NPV = $34,834.5585 Step 2: Determine the annual payments needed to fund college tuition costs. 34834.5585 PV 18 N 9 I/YR PMTOA = ($3,978.5347) QB.101.6

Kitty wants to earn an 18% rate of return on her investment portfolio. How much should she pay for an investment that distributes $1,000 per year for 9 years, with a $3,000 balloon payment at the end of the 10th year? (Round to the nearest dollar) A) $4,494. B) $12,000. C) $4,876. D) $6,234.

C. Kitty should pay no more than the present value of the 9 annual $1,000 payments plus the $3,000 payment at the end of year 10, discounted at 18%. Keystrokes on the HP10BII are as follows: Uneven Cash Flow Method 0 CFj 1000 CFj 9 shift Nj 3000 CFj 18 I/YR shift NPV $4,876.22 QB.101.6

Which of the following statements concerning the internal rate of return on an investment is (are) CORRECT? 1. Generally, if the internal rate of return on an investment is larger than the minimum rate deemed acceptable by the investor, the investment should be rejected. 2. If the internal rate of return on an investment is smaller than the minimum rate deemed acceptable by the investor, the investment should be rejected. A) I only. B) Both I and II. C) II only. D) Neither I nor II

C. Statement I is incorrect because generally, if the internal rate of return on an investment is larger than the minimum rate deemed acceptable by the investor, the investment should be pursued. QB.101.6

Marcy and Dwayne wish to begin a college education savings program for the benefit of their child, Steven, who turned one today. He will begin college at age 18. Currently, college costs are $15,000 per academic year. They assume that college costs will increase at the rate of 5.5% annually from now until Steven enters college and that they can achieve a before-tax rate of return of 7.5% annually on funds earmarked for this purpose. They also assume that Steven will attend college for 4 years. What is the payment that must be made at the end of each year (beginning today) until Steven enters college at age 18? A) $2,735.73 B) $2,544.87 C) $4,494.35 D) $4,632.09

C. The answer is $4,494.35 each year, with keystrokes on the HP10BII/HP10BII+ calculator as follows: Determine the future cost of college for the first year: $15,000 +/− PV 5.5 I/YR 17 N Solve for FV = $37,272.03 Determine the account balance necessary to fund college education: BEG mode $37,272.03 +/− PMT 1.8957 I/YR [(1.075 ÷ 1.055) − 1] × 100 4 N Solve for PV = $144,978.89 Determine the required savings payments: END mode $144,978.89 FV 17 N 7.5 I/YR Solve for PMT = −$4,494.35 QB.101.6

Gina invested in ABC stock that returned 9% the past year. During the year, the inflation rate was 4%. What was Gina's inflation adjusted total return? A) 5.00% B) 9.54% C) 4.81% D) 2.25%

C. The inflation-adjusted rate of return (IAR) formula is sometimes referred to as the real rate of return earned by the investor. That is, it is the nominal (or stated) rate of return of an investment, adjusted for the impact of annual inflation. Therefore, Gina's IAR = [(1 + .09) ÷ (1 + .04)] − 1 = 4.81%. QB.101.6

When determining whether to make an investment in a rental property, Bill is concerned with the discount rate that equates the net investment cash inflows to the net investment cash outflows. Which calculation is Bill using to make this prudent investment decision? A) Future value of an ordinary annuity B) Net present value C) Internal rate of return D) Acid-test ratio

C. The internal rate of return (IRR) is the discount rate that, when applied to the cash flows of an investment, equates the net cash inflows to the net cash outflows. If the IRR calculated is greater than or equal to the investor's required rate of return, then the investor should consider making the investment, all other factors being equal. If the IRR is less than the investor's required rate of return, the investment should not be made. QB.101.6

Maxwell bought a municipal bond that has a 6% coupon rate. He lives in a state other than the one that issued the bond. His state imposes an income tax of 4%. Maxwell is in the 33% federal tax bracket. What is the taxable equivalent yield of this municipal bond? A) 9.52% B) 9.06% C) 8.96% D) 6.25%

C. The taxable equivalent yield of this bond is 8.955% [.06 ÷ (1 − 0.33), rounded to 8.96%. Do not include the 4% state income tax in the calculation because Maxwell lives in a state other than the one that issued the bond. QB.101.6

Angelo refinances his 30-year $250,000 mortgage with a 15-year fixed rate mortgage at an interest rate of 4.75% annually. What is his new monthly payment on this loan? A) $1,304.12 B) $1,973.36 C) $541.21 D) $1,944.58

D. Angelo's monthly payment is $1,944.58 based on a calculation: PV = (250,000) FV = 0 n = 180 (15 × 12) i = .396 (4.75 ÷ 12) PMT = 1,944.58 QB.101.6

Which of the following statements with regards to net present value and internal rate of return is CORRECT? A) If the net present value equals zero, then the internal rate of return is greater than the required rate of return. B) If the net present value equals zero, then the internal rate of return is less than the required rate of return. C) If the net present value is less than zero, then the internal rate of return is greater than the required rate of return. D) If the net present value is greater than zero, then the internal rate of return is greater than the required rate of return.

D. If the net present value is greater than zero, then the internal rate of return is greater than the required rate of return. If the net present value is zero, then the internal rate of return equals the required rate of return. QB.101.6

The rate that produces a net present value of a series of discounted cash flows equal to zero is called the: A) average rate of return. B) cost of capital. C) return on investment (ROI). D) internal rate of return (IRR).

D. The internal rate of return is the rate that produces a net present value of a series of discounted cash flows equal to zero QB.101.6

An investor wants to earn an 18% return. How much should the investor pay for a security that distributes $1,000 per year for nine years, with a $3,000 balloon payment at the end of the 10th year? A) $6,234. B) $4,494. C) $12,000. D)$4,876

D. The investor should pay no more than the present value of the 9 annual $1,000 payments with a $3,000 payment at the end of year 10, discounted at 18%. Uneven Cash Flow Method (HP10BII/10BII+) CF0 = 0 CF1 = 1,000 Nj = 9 CF2 = 3,000 Nj = 1 I/YR = 18 NPV = 4,876.22 QB.101.6

An investor earned a nominal rate of 8% on his investments over the course of last year. If inflation last year was 3.5%, what was the investor's real rate of return? A) 8%. B) 11.5%. C) 4.5%. D) 4.35%.

D. The investor's real (inflation-adjusted) rate of return was 4.35%, calculated as follows: [(1.08 ÷ 1.035) − 1] × 100 = 4.35% QB.101.6