Tutorial topic 6

Question 1

If government bonds are currently paying 8 per cent and the inflation rate is 2.5 per cent, what is the approxiamate real rate? the exact real rate ?

Answer 1

Approximate real rate = 0.08 − 0.025 = 0.055 = 5.5%

Exact real rate = (1.08)/(1.025) − 1 = 0.0537 = 5.37%

Question 2

First investment offers a 14 per cent return. You think that real return will only be 8.55% per cent. What inflation rate is implicit in your calculation?

Answer 2

Expected inflation rate = (1.14)/(1.0855) − 1 = 0.05 = 5%

Question 3

Business shares have an initial price of $6.60 per share, paid a dividend of $0.396 per share during the year, and had an ending price of $5.874 per share. Compute the percentage return.

Answer 3

Percentage return = (5.874 + 0.396 − 6.60)/6.60 × 100%= 5%

Question 4

Business shares have an initial price of $6.60 per share, paid a dividend of $0.396 per share during the year, and had an ending price of $5.874 per share.
What was the dividend yield? The capital gains yield?

Answer 4

Dividend yield = 0.396/6.60 × 100% = 6%

Capital gains yield = (5.874 − 6.60)/6.60 × 100% = 11%

Question 5

Explain why a characteristic of an efficient market is that investments in that market have zero NPV. Why would anyone invest in a market where there are only zero NPVs

Answer 5

On average, the only return that is earned is the required return. There is still a return; however there is no above-normal return and this is the return a positive NPV provides

Question 6

AB has invested $650,000 in WT Super Investment. He has 85% of his funds invested in the diversified portfolio and 15% invested in the fixed-interest portfolio. He withdraws $48,000. at the end of each year for his living expenses. Even though the current rate of inflation 5%., AB finds that this is sufficient money for hime to live comfortably and spend time at his club. The earnings of the portfolios per year have been:

Diversified: 14%

Fixed-interest: 3%

It is expected that these rates will continue into the foreseeable future.

a. If the portfolios continued to earn the same rate, does AB’s withdrawal allow him to stay in front of inflation and not be withdrawing his real capital?
b. What would be the necessary split of funds across the portfolios that AB would have to maintain so that his current withdrawals match inflation?

Answer 6

a Annual nominal earnings (R) = 0.1235

Real earnings (r)	= 0.07
Annual withdrawal rate ( w )	= 48 000/650000
						= 0.07384 Excess of withdrawal rate over real rate = 0.07 − 0.07384 = 0.0038 = 0.38%

The withdrawal rate is just above the real earnings rate which means real capital is decreasing each year.

b	Rate to provide current withdrawals plus inflation = [(1 + R)(1 + h)] − 1
	= [1.07384 × 1.05] – 1
	= 0.127538

Let x be the proportion to be invested in the diversified portfolio to earn 14% or 0.14

0.127538 = 0.14x + (1 – x) 0.03
0.127538 − 0.03 = 0.14x – 0.03x
0.097538 = 0.11x
0.8867 = x
so that 88.67 % is invested in the diversified portfolio
and 11.33 % invested in the fixed portfolio.

Expected nominal return =.8867 × 0.14 + 0.1133 ×0.03
=.1241 + 0.0034
= 0.1275

Expected real return = 1.1275/1.05 = 1.738
Withdrawal rate= 0.0738 as above