Question

q27. a) you are planning to buy a new caravan to make a trip around australia. the cost of the van is $225000 and you can get a loan from the bank for that amount. if you can get a fifteen year loan at 8.75% per annum compounded fortnightly, how much do you need to pay every fortnight?

b) suppose you are going to receive $2000 per year for five years. the appropriate interest is 6% per annum. what is the future value if the payments are an annuity due?

c) what is the value of a 9% bond that matures in 5 years, pays interest semi-annually, has a face value of $1000, when the current market yield is 5.5% per annum?

d) jerry's airport pickup service is a fast growth stock and expects to grow at an annual rate of 25$ for the next 4 years. it then will settle to a constant-growth rate of 8%. the last year dividend was $4. if the required rate of return is 18$, what is the current price of the stock? (draw a timeline too)

Answer 1

a)

One year = 26.07 Fortnight

Interest Rate = 8.75%

Interest Rate per Fortnight = 8.75%/26.07

= 0.34%(Approx) per fortnight

PVAF (0.34%, 391 periods) = 216.11

Cost of Van = $225,000

Payment for every fortnight = $225,000/216.11

= $1,041.14 (Approx)

b)

Year	Cash Flow	Interest	Future Value
1	$      2,000	1.2625	$        2,525
2	$      2,000	1.1910	$        2,382
3	$      2,000	1.1236	$        2,247
4	$      2,000	1.0600	$        2,120
5	$      2,000	1.0000	$        2,000
	Total Future Value		$      11,274

Future value = $11,274

c)

Period	Type	Cashflow	Yeild @5.5% or 2.75% semianual	Value
1	Interest	$           45	1.2765	$            57
2	Interest	$           45	1.2424	$            56
3	Interest	$           45	1.2091	$            54
4	Interest	$           45	1.1768	$            53
5	Interest	$           45	1.1453	$            52
6	Interest	$           45	1.1146	$            50
7	Interest	$           45	1.0848	$            49
8	Interest	$           45	1.0558	$            48
9	Interest	$           45	1.0275	$            46
10	Interest	$           45	1.0000	$            45
10	Maturity	$      1,000	1.0000	$      1,000
		Value of Bond		$      1,510

Value of Bond = $1,510

d)

Growth Rate = 8%

Dividend D0 = $4

Required Rate of return = 18%

Current price of stock = D1/(Ke-g)

= $4(1.08)/0.18-0.08

= $4.32/0.1

= $43.20

Current Price of stock = $43.20