Chap 6 Knowledge Check Solutions

Knowledge Check 6.1

Time	Interest	Deposit	Withdrawal	Balance
0		$200,000		$200,000
1	$40,000	40,000		280,000
2	56,000		50,000	286,00
3	57,200		50,000	293,200
4	58,640		50,000	301,840
5	60,368		300,000	62,208

Note that $62,208 is the future value of $25,000!

Knowledge Check 6.2

At 15% effective:

We have the outflows:

Year 0: $P V ($ 200, 000) = $ 200, 000$
Year 1: $P V ($ 40, 000) = \frac{$ 40, 000}{{1.15}^{1}} = $ 34, 782.61$
Total PV(Outflows) = $234,782.61

And the Inflows:

Year 2: $P V ($ 50, 000) = \frac{$ 50, 000}{{1.15}^{2}} = $ 37, 807.18$
Year 3: $P V ($ 50, 000) = \frac{$ 50, 000}{{1.15}^{3}} = $ 32, 875.81$
Year 4: $P V ($ 50, 000) = \frac{$ 50, 000}{{1.15}^{4}} = $ 28, 587.66$
Year 5: $P V ($ 300, 000) = \frac{$ 300, 000}{{1.15}^{5}} = $ 149, 153.02$
Total PV Inflows = $248,423.68

So that

$\begin{aligned} N P V & = P V_{I n f l o w s} - P V_{O u t f l o w s} \\ = $ 234, 782.61 - 248, 423.68 \\ = $ 13, 641.68 \end{aligned}$

Since the NPV is positive, the investment would be acceptable at 15% effective.

Knowledge Check 6.3

Option A

Time (yr)	Cash Flow	PV
0	-$30,000	$- $ 30, 000$
1	12,000	$\frac{12, 000}{{1.20}^{1}} = 10, 000$
2	12,000	$\frac{12, 000}{{1.20}^{2}} = 8, 333.33$
3	12,000	$\frac{12, 000}{{1.20}^{3}} = 6, 944.44$
4	26,000	$\frac{26, 000}{{1.20}^{4}} = 12, 538.58$

	NPV =	$$ 7, 816.36$

Option B

Time (yr)	Cash Flow	PV
0	-$92,000	$- $ 92, 000$
1	21,000	$\frac{21, 000}{{1.20}^{1}} = 17, 500$
2	21,000	$\frac{21, 000}{{1.20}^{2}} = 14, 583.33$
3	21,000	$\frac{21, 000}{{1.20}^{3}} = 12, 152.78$
4	21,000	$\frac{21, 000}{{1.20}^{4}} = 10, 127.31$
5	21,000+95,000	$\frac{116, 000}{{1.20}^{5}} = 46, 617.80$

	NPV =	$$ 8, 981.22$

Knowledge Check 6.4

Option A:

Time (yr)	Cash Flow	BALANCE
0	$- $ 30, 000$	$- $ 30, 000$
1	$12, 000$	$- 30, 000 + 12, 000 = - 18, 000$
2	$12, 000$	$- 18, 000 + 12, 000 = - 6, 000$
3	$12, 000$	$- 6, 000 + 12, 000 = 6, 000$
4	$26, 000$	$6, 000 + 26, 000 = 32, 000$

Payback is reached halfway between years 2 and 3, so we use a value of 2.5

Option B

Time (yr)	Cash Flow	BALANCE
0	$- $ 92, 000$
1	$21, 000$	$- 92, 000 + 21, 000 = - 71, 000$
2	$21, 000$	$- 71, 000 + 21, 000 = - 50, 000$
3	$21, 000$	$- 50, 000 + 21, 000 = - 29, 000$
4	$21, 000$	$- 29, 000 + 21, 000 = - 8, 000$
5	$21, 000 + 95, 000$	$- 8, 000 + 116, 000 = 108, 000$

Here we are in between years 4 and 5. To approximate we use:

$P a y b a c k = 4 + \frac{$ 8, 000}{$ 116, 000} = 4.07 years$

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