episode 03 exercise answer 01

Part 1: Solution

Let's see how well you answered the questions.

	1.	As she works with rates of return, Maria is using mathematical techniques that quantify the time value of money. The time value of money depends on several factors, including the following: when the money will change hands, the amount that's invested or borrowed, the interest rate, and the frequency of compounding. If Maria wishes to borrow money, which of the following offers is most advantageous from a time-value point of view?
		a. Daily compounding with a nominal annual interest rate of 12%.
		b. Semi-annual compounding with a nominal interest rate of 12%.
		c. Semi-annual compounding with a nominal interest rate of 13%.
		d. Daily compounding with a nominal annual interest rate of 13%.
		Your Answer:
		Correct Answer: b
		Financial decisions should be based on effective annual rates of interest that take into consideration compounding, rather than nominal interest rates. All else the same, more frequent compounding raises the effective annual rate. Semi-annual compounding means that interest will be compounded twice per year for an effective annual rate of 12.36%. Daily compounding of a 12% annual rate will yield 12.748%, using a 365-day year. Both of the 13% alternatives will yield effective annual rates in excess of 13%. Therefore, a borrower who wants the lowest cost of borrowing should choose b.

	2.	When Maria discusses her parents' retirement strategy, she suggests that it is not enough simply to target how much one saves. One must also carefully consider what type of investment one will make with those savings. She discusses bank certificates of deposit, corporate bonds, and stocks. Maria says that bonds will earn about 2% more per year than CDs, and stocks will earn an average return that is higher than bonds. Corporate bonds tend to have lower rates of return than corporate common stock because they tend to be
		a. higher risk.
		b. worth more.
		c. less risky.
		d. longer term.
		Your Answer:
		Correct Answer: c
		Investors demand higher expected returns from higher risk investments. Therefore, stocks, which are generally riskier than bonds, will tend to have higher rates of return.

	3.	Cash flows with higher risk will have
		a. lower present value than low risk cash flows, all else the same.
		b. lower expected future value than low risk cash flows, all else the same.
		c. higher present value than low risk cash flows, all else the same.
		d. higher expected future value than low risk cash flows, all else the same.
		e. a and c.
		f. a and d.
		g. b and d.
		Your Answer:
		Correct Answer: f
		Cash flows that are high risk have a higher required return (or discount rate) than do low risk cash flows. Higher rates of return make present values low and expected future values high.

	4.	A perpetuity is:
		a. like an ordinary annuity except that the payments continue indefinitely.
		b. worth less than an ordinary annuity of equal risk and making equal payments.
		c. like an annuity due except that the payments continue indefinitely.
		d. more difficult to value than an annuity.
		Your Answer:
		Correct Answer: a
		A perpetuity is a stream of equal payments made at equal time intervals which continue indefinitely. The general assumption is that the first payment is made at the end of the first period.

	5.	Find the present value of $5,000 to be received in 36 months, if the interest rate is 12% per year, compounded monthly.
		a. $84.55
		b. $3,558.90
		c. $3,494.62
		d. none of the above
		Your Answer:
		Correct Answer: c
		The first answer, $84.55, is the result of finding the present value of $5,000 due in 36 months if the interest rate is 12% per month. So, if you choose this result, it means that you forgot to convert the annual rate to a monthly rate. Answer b is determined by discounting $5,000 for 3 years at 12% per year, and therefore doesn't reflect monthly compounding effects.

	6.	Maria's parents plan to rent an apartment when they retire. The apartment is part of a retirement center and rents for $500 a month, payable in advance. If her parents can earn 8% per year on any amount deposited in a special savings account, how much would they need to deposit in that account today in order to fully fund the rental requirements for the coming 12 months? (Hint: Assume that they will include the first month's rent in the deposit even though the money will only be in the account momentarily before it is used to pay the rent.)
		a. $5,786.21
		b. $5,747.89
		c. $4,069.48
		d. $3,768.04
		Your Answer:
		Correct Answer: a
		It is an annuity due because the rent is payable in advance (at the beginning of each month). The 8% annual rate must be adjusted to a monthly rate reflecting the monthly payments. If you answered b, you did the problem as an ordinary annuity. If you answered c, you did the problem using a monthly rate of 8%, meaning that you forgot to convert the 8% by dividing it by 12. Finally, if you answered d, then you did not convert the 8% and you also did the problem as an ordinary annuity.

	7.	A British Consol bond is a security that pays its holder a fixed amount every year forever. Suppose Maria's parents own such a bond that pays them 150 British pounds annually and is selling for 2,000 pounds. What discount rate must investors apply to this bond as they determine its value?
		a. There is not enough information to estimate the discount rate.
		b. 7.5%
		c. .075%
		d. 13.33%
		Your Answer:
		Correct Answer: b
		The consol bond is a perpetuity since it pays a fixed stream of payments in perpetuity. To arrive at the correct rate of 7.5%, simply divide the price by the payment amount. If you answered c, then you divided but forgot to convert the decimal answer to a percentage. If you answered d, then you divided the price by the payment amount (and you also assumed that the answer was in percentage terms, which is incorrect).

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