Question

At the beginning of 1976 a relative migrated to Australia with $10,000 ‘spare cash’. The money could have been used to buy a block of land or invested in an ‘at-call’ savings account that paid interest at 8% p.a. compounded half-yearly. At the end of 2018, the land was valued by a local real estate agent who was keen to list the property on behalf of his agency, at a price of approximately $400,000.

Required:

1. a) Which of the alternative investments had the higher value at the end of 2018? Justify your response with appropriate calculations.

(Students should write no more than 50 words for this part of the question).

b) i) Assuming the half-yearly compounding of interest, what was the rate of growth in the land value over the total period expressed as a nominal annual interest rate?

ii) What was the rate of growth in the land value over the total period expressed as an effective interest rate?

iii) What was the rate of growth in the ‘at-call’ savings account over the total period expressed as an effective interest rate?

1. c) What investment in the savings account would have been necessary at the beginning of 1976, to have the same value as the land was worth at the end of 2018? Briefly explain your response.

(Students should write no more than 50 words for this part of the question).

d) Recognising both your finance skills and ‘common sense’, one of your friends has asked whether your calculations above allow you to determine which of the investments would have been ‘better’ to make at the beginning of 1976, given the outcomes discussed above at the end of 2018. Provide a well-reasoned, complete response to this question taking into consideration various financial and non-financial issues.

(Students should write no more than 100 words for this part of the question).

1. d) i) You have now been provided further information that the investment in the land required the owner to make continuous annual payments of council rates over the total period held. These amounts are determined in accordance with Table 1 below. Assuming the land was sold at the end of 2018 (but ignoring the expected sale value), what is the adjusted present value at the beginning of 1976 of all the cash outflows relating to the acquisition and continued ownership of the land?

Note: For the purposes of this question assume the following:

1. Rates are payable on the anniversary of each year of land ownership.

2. The annual amount of the rates are determined in accordance with the following formula;

Initial Purchase Cost ($) x Factor (times) x Relevant Percentage (%)

3. Rates are still payable for the 2018 year (for the full year).

Anniversary number of years land held	Factor (times)	Relevant Percentage (%)
1 to 5 years	1.0	1.5
6 to 10 years	1.5	1.5
11 to 15 years	3.0	1.0
16 to 20 years	6.0	1.0
21 to 25 years	10.0	0.8
26 to 30 years	20.0	0.8
31 to 35 years	25.0	0.6
36 to 40 years	30.0	0.6
41 to 45 years	40.0	0.4

Table 1

ii) Taking into consideration the calculations from part e) i) of this question, what is the rate of growth in the land value over the total period expressed as an effective interest rate?

(Students should write no more than 50 words for this part of the question).

Answer 1

(1) (a) Beginning Year = 1976 and Ending Year = 2018, Savings Tenure = 2018 - 1975 = 43 years

Initial Land Value = $ 10000 and Final Land Value = $ 400000

Savings Account Rate = 8 % compounded semi-annually

Value of Savings Account = 10000 x [1+(0.08/2)]^(43 x 2) = $ 291653.49

As is observable, the land has a higher value

(b) (i) Let the half-yearly compounded nominal annual rate be 2r%

Therefore, 10000 x [1+r]^(43 x 2) = 400000

1+r = 1.04383

r = 0.04383 or 4.383 %

Nominal Annual Rate = 2 x 4.383 = 8.766 %

(ii) Effective Annual Growth Rate of Land Value = [1.04383]^(2) - 1 = 0.089576 or 8.9576 % ~ 8.96 %

(iii) Effective Annual Rate of Savings Account = [1.04]^(2) - 1 = 0.0816 or 8.16 %

(c) Required Initial Investment = $ R, Final Target Value = $ 400000 and Tenure = 43 x 2 = 86 half-years

Interest Rate = 8 % per annum compounded half-yearly

Therefore, R x [1+(0.08/2)]^(86) = 400000

R = 13714.91

NOTE: Please raise a separate query for the solution to the second unrelated question as one query is restricted to the solution of only one complete question with up to four sub-parts.