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Chapter 17: Q2. (page 369)

It is a fact that (1 + 0.12)3 = 1.40. Knowing that to be true, what is the present value of \(140 received in three years if the annual interest rate is 12 percent?

  1. \)1.40

  2. \(12

  3. \)100

  4. $112

Short Answer

Expert verified

Option (c) $100

Step by step solution

01

Step 1. Meaning and formula for the present value

The present value method says that the current value of the amount received in the future is the ratio of the future amount to the compound interest gained over the years.

X0=Xt1+it

X0 is the present value of the future amount, i is the interest rate, t is the time, and Xt is the amount received after t years.

02

Step 2. Calculations for the answer

Given that $140 will be received after 3 years along with the compound interest charged by 12% annually, the present value of $140 is:

X0=1401+0.123=1401.40=100

Hence, the answer is $100.

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Most popular questions from this chapter

Suppose that the equation for the SLM is Y = 0.05 + 0.04X, where Y is the average expected rate of return, 0.05 is the vertical intercept, 0.04 is the slope, and X is the risk level as measured by beta. What is the risk-free interest rate for this SML? What is the average expected rate of return at a beta of 1.5? What is the value of beta at an average expected rate of return is 7 percent?

If an investment has 35 percent more non-diversifiable risk than the market portfolio, its beta will be:

  1. 35

  2. 1.35

  3. 0.35

Identify each of the following investments as either an economic investment or a financial investment.

a. A company builds a new factory.

b. A pension plan buys some Google stock.

c. A mining company sets up a new gold mine.

d. A woman buys a 100-year-old farmhouse in the countryside.

e. A man buys a newly built home in the city.

f. A company buys an old factory.

Next, consider another pair of assets, C and D. Asset C will make a single payment of \(150 in one year while D will make a single payment of \)200 in one year. Assume that the current price of C is \(120 and that the current price of D is \)180.

c. What are the rates of return of assets C and D at their current prices? Given these rates of return, which asset should investors buy and which asset should they sell?

d. Assume that arbitrage continues until C and D have the same expected rate of return. When arbitrage ends, will C and D have the same price?

Compare your answers to questions a through d before answering question e.

e. We know that arbitrage will equalize rates of return. Does it also guarantee to equalize prices? In what situations will it equalize prices?

Why is it so hard for actively managed funds to generate higher rates of return than passively managed index funds having similar levels of risk? Is there a simple way for an actively managed fund to increase its average expected rate of return?
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