Question

A pine plantation returns nothing to its owner in the first 3 years. In the following 2 years, the returns are $100,000 (year 4) and $150,000 (year 5), respectively, and then the return is $200,000 per year in perpetuity from year 6 onwards. The returns can be invested at 8% per annum.  What is the present value to the owner (the value in year 0)?

	a.	The present value to the owner is $2,189,389.32.
	b.	The present value to the owner is $2,027,212.33.
	c.	The present value to the owner is $2,364,540.47.
	d.	The present value to the owner is $1,877,048.46.

Answer 1

Calculation of present value of the owner
Year	Cash flow	Discount factor @ 8%	Present Values
A	B	C	B*C
0	$0.00	1	$0.00
1	$0.00	0.925926	$0.00
2	$0.00	0.857339	$0.00
3	$0.00	0.793832	$0.00
4	$100,000.00	0.73503	$73,502.99
5	$150,000.00	0.680583	$102,087.48
Value of perpetuity	$2,500,000.00	0.680583	$1,701,457.99
Present value of the owner			$1,877,048.46
The answer is Option d.
Working
Present value at the end of 5th year of perpetuity of $200000 per year from Year 6 onwards = Annuity / Rate of return = $200000/8% = $25,00,000