IAS 282 Class test 8 memo

Department of Actuarial Science

University of Pretoria

Actuarial Mathematics 282

Class test 8(group) memo

Date: 6 October 2022

Question 2 [4 Marks]

Your friend, Steve, is considering investing in the ordinary shares of ABC inc. The current price of the

shares is R12 per share. ABC inc. is a relatively new company so it is highly unlikely that the share will pay

any dividends in the next five years. However, Steve expects the company to pay a dividend of R2 per

share in exactly six years’ time, R2.50 per share in exactly seven years’ time, with annual dividends

increasing thereafter by 1% per annum in perpetuity.

Steve is subject to income tax at a rate of 10% per annum and capital gains tax at a rate of 15% of any

capital gain realized. Both income tax and capital gains tax are payable as and when the cashflow occurs.

In five years’ time, Steve expects to sell the shares. The sale price is expected to be equal to the present

value of the expected dividends from the share at that time at a rate of interest of 8% per annum

effective.

a) Calculate the effective gross rate of return per annum Steve will obtain if he buys the share and

then sells it at the expected price in five years’ time. [4]

Question 3 [6 Marks]

A residential property is available for R250 000, and you decide to use your savings to purchase this

property. Transfer and attorney costs will be an additional R100 000.

You will receive rental income of R2 500 per month payable in advance, and this will escalate annually by

7.5%. You do not intend to sell this property and you will therefore receive the income into perpetuity.

Monthly levies, including all maintenance costs on the property will amount to R1 000 payable in arrears,

and this will include all maintenance costs on the property. You assume this will also increase annually by

7.5%.

You are taxed on income at a rate of 30%, and capital gains are taxed at 15%. Both income tax and capital

gains tax are payable as and when the cashflows occur. Note that your taxable income will be defined as

any income earned less the levies and maintenance costs incurred on the property. Also note that you

will only be taxed once your annual taxable income is equal to or more than R50,000 per annum and that

you will be taxed on your total taxable income (i.e. the first R50 000 is not exempt from tax). Until then,

you will not be taxed.

Calculate the price that you will be willing to pay for the property assuming you require an annualised

nominal net yield of 10% after allowance for expenses. [6]

Actuarial Science (IAS 282)

University of Pretoria

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