3.4 ValuingCashFlowsatDifferentPointsinTime

Sara wants to have $600,000 in her savings account when she retires. How much must she put in the account now, if the account pays a fixed interest rate of 8%, to ensure that she has $600,000 in 20 years? A) $128,729 B) $180,221 C) $231,712 D) $139,541

A) Calculate the PV with FV = $600,000, N = 20, and interest = 8%, which = $128,729.

Which of the following statements is FALSE about valuing cash at different points in time? A) Finding the present value (PV) and compounding are the same. B) A dollar today and a dollar in one year are not equivalent. C) If you want to compare or combine cash flows that occur at different points in time, you first need to convert the cash flows into the same units or move them to the same point in time. D) The equivalent value of two cash flows at two different points in time is sometimes referred to as the time value of money.

A) Finding the present value (PV) and discounting are the same.

If the current market rate of interest is 8%, then the present value (PV) of this timeline as of year 0 is closest to ________. A) $502 B) $653 C) $600 D) $1004

A) PV = FV(1 + r)n 100 / (1.08)1 = 92.59 200 / (1.08)2 = 171.47 300 / (1.08)3 = 238.15 Sum = $502.21, which is approximately $502.

Why should interest rates be generally positive?

An investor should be compensated for foregoing current consumption and, everything else remaining the same, a positive interest rate serves to compensate the investor.

If an analyst incorrectly adds cash flows occurring at different points in time, what is the implied assumption in the process?

Answer: Cash flows occurring at different points in time cannot be added because a dollar today is worth more than a dollar tomorrow. In other words, these cash flows are not in the same units. The compounding and discounting effect causes these cash flows to be different across time. However, this is only valid for nonzero interest rates. Hence, the implied assumption in adding cash flows across time is that interest rate is zero.

On the day Harry was born, his parents put $1200 into an investment account that promises to pay a fixed interest rate of 6 percent per year. How much money will Harry have in this account when he turns 21? A) $3263 B) $4079 C) $8158 D) $3766

B) Calculate the FV with PV = $1200, interest = 6%, and N = 21, which = $4079.

What is the present value (PV) of $100,000 received six years from now, assuming the interest rate is 8% per year? A) $60,000.00 B) $63,016.96 C) $78,771.20 D) $110,279.68

B) Calculate the PV with FV = $100,000, interest = 8%, and N = 6, which = $63,016.96.

If the current market rate of interest is 13%, then the value of the cash flows in year 0 and year 2 as of year 1 is closest to ________. A) $167.35 B) -$98.7 C) $98.7 D) -$70

B) This is a two part problem involving both present and future values. FV of year 0 c/f = FV = PV(1 + r)n = -150(1.13)1 = -$169.50 PV of year 2 c/f = PV = FV / (1 + r)n = 80 / (1.13)1 = $70.80 So, the answer is -$169.50 + $70.80 = -$98.7

20) To compute the future value of a cash flow, you must ________. A) discount it B) compound it C) double it D) arbitrage it

B.

An investment will pay you $120 in one year and $200 in two years. If the interest rate is 4%, what is the present value of these cash flows? A) $304.91 B) $307.69 C) $300.29 D) $320.00

C) 120/(1.04) + 200/(1.042) = 115.38 + 184.91 = 300.29

What is the future value (FV) of $20,000 in four years, assuming the interest rate is 4% per year? A) $15,208.16 B) $19,887.59 C) $23,397.17 D) $25,736.89

C) Calculate the FV with PV = $20,000,interest = 4%, and N = 4, which = $23,397.17.

What is the present value (PV) of $50,000 received twenty years from now, assuming the interest rate is 6% per year? A) $32,500.00 B) $13,251.70 C) $15,590.24 D) $27,282.92

C) Calculate the PV with FV = $50,000, interest = 6%, and N = 20, which = $15,590.24.

What is the present value (PV) of $90,000 received six years from now, assuming the interest rate is 5% per year? A) $58,500.00 B) $57,085.48 C) $67,159.39 D) $117,528.93

C) Calculate the PV with FV = $90,000, interest = 5%, and N = 6, which = $67,159.39.

the N using the rule of 72. Then, N = 72/8 = 9 years.

C) CalculatewithFV=$1350,interest=4%,andnumberofyears=5, which gives PV = $1109.60

If money is invested at 8% per year, after approximately how many years will the interest earned be equal to the original investment? A) 7 years B) 8 years C) 9 years D) 11 years

C. calculate the N using the rule of 72. Then, N = 72/8 = 9 years.

If $17,000 is invested at 10% per year, in approximately how many years will the investment double? A) 7.3 years B) 8.4 years C) 11.0 years D) 14.6 years

Calculate the N with FV = $34,000, PV = $17,000, and interest = 10%, which = 7.3 years

What is the future value (FV) of $50,000 in thirty years, assuming the interest rate is 12% per year? A) $32,500.00 B) $1,273,296.69 C) $1,348,196.50 D) $1,497,996.11

D ) Calculate the FV with PV = $50,000, interest = 12%, and N = 30, which = $1,497,996.11.

15) Which of the following statements is FALSE about valuing cash at different points in time? A) The process of moving forward along the timeline to determine a cash flowʹs value in the future is known as compounding. B) The effect of earning interest on interest is known as compound interest. C) It is only possible to compare or combine values at the same point in time. D) A dollar in the future is worth more than a dollar today.

D) A dollar in the future is worth less than a dollar today.

What is the future value (FV) of $50,000 in thirty years, assuming the interest rate is 6% per year? A) $32,500.00 B) $244,098.38 C) $258,457.10 D) $287,174.56

D) Calculate the FV with PV = $50,000,interest = 6%, and N = 30, which = $287,174.56.

If the current market rate of interest is 7%, then the value as of year 1 is closest to ________. A) $0B) $1000 C) $570 D) $68

D) Two part problem: FV = PV (1 + r)n = 500(1.07)1 = $535 PV = FV / (1 + r)n = -500 / (1.07)1 = -$467 So, the answer is $535 + -$467 = $68.

A dollar today and a dollar in one year may be considered to be equivalent.

F

To calculate a cash flowʹs present value (PV), you must compound it.

F