Question

Please give me solution and pick from multiple choice

You are offered an investment that will pay you $200 in year 1, $400 in year 2, $600 in year 3 and $800 in year 4. You can earn 10% per annum on very similar investment. Calculate the present value of this investment.

	a.	The present value of investment is $2000.
	b.	The present value of investment is $1509.60.
	c.	The present value of investment is $963.19.
	d.	The present value of investment is $1660.56.

Phantom Limited borrows $150,000 at an interest rate of 12% per annum compounding quarterly, repayable by equal quarterly instalments over 30 years. Calculate the principal and interest components of the first repayment.

	a.	For the first repayment, the principal component is $101.09 and interest component is $4,500.
	b.	For the first repayment, the principal component is $133.49 and interest component is $4,500.
	c.	For the first repayment, the principal component is $133.49 and interest component is $4,200.
	d.	For the first repayment, the principal component is $101.09 and interest component is $4,200.

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

Answer 1

Present value of investment is equal to discounted value of future cash flows

= 200/(1.1) + 400/(1.1)² + 600/(1.1)³ + 800/(1.1)⁴

= $1,509.60

Hence, the answer is b.

Quarterly rate of interest = 12%*4/12 = 3%

Number of quarters = 30*4 = 120

Payment Amount = 150,000/PVAF(3%, 120 periods)

= 150,000/32.37302258

= $4,633.49

Interest Component = 150,000*3% = $4,500

Principal Repaid = 4,633.49 – 4,500

= $133.49

Hence, the answer is b.

Present value = 100,000/(1.08)⁴ + 150,000/(1.08)⁵ + 200,000/8%*(1.08)⁵

= $1,877,048.46

Hence, the answer is c.