Chapter 6 - Discounted Cash Flows and Valuation

Computing annuity payment: Trevor Smith wants to have a million dollars at retirement, which is 15 years away. He already has $200,000 in an IRA earning 8 percent annually. How much does he need to save each year, beginning at the end of this year to reach his target? Assume he could earn 8 percent on any investment he makes. (Round to the nearest dollar.)

$13,464

Perpetuity: Your father is 60 years old and wants to set up a cash flow stream that would be forever. He would like to receive $20,000 every year, beginning at the end of this year. If he could invest in account earning 9 percent, how much would he have to invest today to receive his perpetual cash flow? (Round to the nearest dollar.)

$222,222 PVP₀ = CF ÷ i = $20000 ÷ .09 = $222,222

Present value of an annuity: Lorraine Jackson won a lottery. She will have a choice of receiving $25,000 at the end of each year for the next 30 years, or a lump sum today. If she can earn a return of 10 percent on any investment she makes, what is the minimum amount she should be willing to accept today as a lump-sum payment? (Round to the nearest hundred dollars.)

$235,700

Growing perpetuity: Jack Benny is planning to invest in an insurance company product. The product will pay $10,000 at the end of this year. Thereafter, the payments will grow annually at a 3 percent rate forever. Jack will be able to invest his cash flows at a rate of 6.5 percent. What is the present value of this investment cash flow stream? (Round to the nearest dollar.)

$285,714 PVP = CF₁ ÷ (i - g) PVP = 10000 ÷ (.065 - .03) PVP = 10000 ÷ .035 PVP = 285714

Future value of an annuity: Jayadev Athreya has started on his first job. He plans to start saving for retirement early. He will invest $5,000 at the end of each year for the next 45 years in a fund that will earn a return of 10 percent. How much will Jayadev have at the end of 45 years? (Round to the nearest dollar.)

$3,594,524

Computing annuity payment: Maricela Sanchez needs to have $25,000 in five years. If she can earn 8 percent on any investment, what is the amount that she will have to invest every year at the end of each year for the next five years? (Round to the nearest dollar.)

$4,261

Computing annuity payment: Jackson Electricals has borrowed $27,850 from its bank at an annual rate of 8.5 percent. It plans to repay the loan in eight equal installments, beginning in a year. What is its annual loan payment? (Round to the nearest dollar.)

$4,939

Annuity due: You plan to save $1,400 for the next four years, beginning now, to pay for a vacation. If you can invest it at 6 percent, how much will you have at the end of four years? (Round to the nearest dollar.)

$6,492

FV of multiple cash flows: Chandler Corp. is expecting a new project to start producing cash flows, beginning at the end of this year. They expect cash flows to be as follows: 1 = $643,547 2 = $678,214 3 = $775,908 4 = $778,326 5 = $735,444 If they can reinvest these cash flows to earn a return of 8.2 percent, what is the future value of this cash flow stream at the end of five years? (Round to the nearest dollar.)

FV₅=[643547 x (1.082)⁴] + [678214 x 91.082)³] + [775908 x (1.082)²] + [778326 x (1.082)] + 735444 FV₅= 882042 + 859109 + 908374 + 842149 + 735444 FV₅ = $4,227,118

Perpetuity: Chris Collinge has funded a retirement investment with $250,000 earning a return of 5.75 percent. What is the value of the payment that he can receive in perpetuity? (Round to the nearest dollar.)

Feedback: Annual payment needed = PMT Present value of investment = PVA = $250,000 Investment rate of return = i = 5.75% Term of payment = Perpetuity

Growing annuity: Hill Enterprises is expecting tremendous growth from its newest boutique store. Next year the store is expected to bring in net cash flows of $675,000. The company expects its earnings to grow annually at a rate of 13 percent for the next 15 years. What is the present value of this growing annuity if the firm uses a discount rate of 18 percent on its investments? (Round to the nearest dollar.)

Feedback: Time of growth = n = 15 years Next year's expected net cash flow = CF1 = $675,000 Expected annual growth rate = g = 13% Firm's required rate of return = i = 18% Present value of growing annuity = PVAn

Present value of an annuity: Herm Mueller has invested in a fund that will provide him a cash flow of $11,700 for the next 20 years. If his opportunity cost is 8.5 percent, what is the present value of this cash flow stream? (Round to the nearest dollar.)

PVA₂₀ = (117000 ÷ .085) X [1- (1 ÷ 1.085)²⁰] PVA₂₀ = 137647.0588 X .8043836116 PVA₂₀ = $110,721

PV of multiple cash flows: Ajax Corp. is expecting the following cash flows—$79,000, $112,000, $164,000, $84,000, and $242,000—over the next five years. If the company's opportunity cost is 15 percent, what is the present value of these cash flows? (Round to the nearest dollar.)

PV₅ = (79000 ÷ 1.15) + [112000 ÷ (1.15)²] + [164000 ÷ (1.15)³] + [84000 ÷ (1.15)⁴] + [242000 ÷ (1.15)⁵] PV₅ = 68695.65 + 84688.09 + 107832.66 + 48027.27 + 120316.76 PV₅ = $429,560

Which one of the following statements is TRUE about the effective annual rate (EAR)?

The EAR conversion formula accounts for the number of compounding periods and, thus, effectively adjusts the annualized interest rate for the time value of money. *****All of these are true. The EAR is the true cost of borrowing and lending. The effective annual interest rate (EAR) is defined as the annual growth rate that takes compounding into account.

Which one of the following statements is NOT true?

The EAR takes compounding into account. The EAR is the appropriate rate to do present and future value calculations. *****The APR is the appropriate rate to do present and future value calculations. The EAR is the true cost of borrowing and lending.

Which one of the following statements is NOT true about amortization?

With an amortized loan, a smaller proportion of each month's payment goes toward interest in the early periods

Cash flows associated with annuities are considered to be

a cash flow stream of the same amount (a constant cash flow stream).

Your investment in a small business venture will produce cash flows that increase by 15 percent every year for the next 25 years. This cash flow stream is called

a growing annuity.

A firm receives a cash flow from an investment that will increase by 10 percent annually for an infinite number of years. This cash flow stream is called

a growing perpetuity.

Effective annual rate: Largent Supplies Corp. has borrowed to invest in a project. The loan calls for a payment of $17,384 every month for three years. The lender quoted Largent a rate of 8.40 percent with monthly compounding. At what rate would you discount the payments to find amount borrowed by Largent? (Round to two decimal places.)

monthly interest rate = 8.4 / 12 = 0.7 % = 0.007 effective anuual rate = ( 1 + 0.007)^12 -1 = 1.0873107 -1 = 0.0873107 = 8.73 %