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: [latex]PV($200,000)= $200,000[/latex]
- Year 1: [latex]PV($40,000) = \frac{$40,000}{1.15^1} = $34,782.61[/latex]
- Total PV(Outflows) = $234,782.61
And the Inflows:
- Year 2: [latex]PV($50,000) = \frac{$50,000}{1.15^2} = $37,807.18[/latex]
- Year 3: [latex]PV($50,000) = \frac{$50,000}{1.15^3} = $32,875.81[/latex]
- Year 4: [latex]PV($50,000) = \frac{$50,000}{1.15^4} = $28,587.66[/latex]
- Year 5: [latex]PV($300,000) = \frac{$300,000}{1.15^5} = $149,153.02[/latex]
- Total PV Inflows = $248,423.68
So that
[latex]\begin{align*} NPV &=PV_{Inflows} - PV_{Outflows}\\ &=$234,782.61-248,423.68\\ &=$13,641.68 \end{align*}[/latex]
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 | [latex]-$30,000[/latex] | \(-$30,000\) |
| 1 | [latex]12,000[/latex] | \(-30,000+12,000 = -18,000\) |
| 2 | [latex]12,000[/latex] | \(-18,000+12,000=-6,000\) |
| 3 | [latex]12,000[/latex] | \(-6,000+12,000 = 6,000\) |
| 4 | [latex]26,000[/latex] | \(6,000+26,000=32,000\) |
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 | [latex]-$92,000[/latex] | |
| 1 | [latex]21,000[/latex] | \(-92,000 + 21,000= -71,000\) |
| 2 | [latex]21,000[/latex] | \(-71,000+21,000 = -50,000\) |
| 3 | [latex]21,000[/latex] | \(-50,000+21,000 = -29,000\) |
| 4 | [latex]21,000[/latex] | \(-29,000+21,000 = -8,000\) |
| 5 | [latex]21,000+95,000[/latex] | \(-8,000+116,000=108,000\) |
Here we are in between years 4 and 5. To approximate we use:
\[Payback = 4 + \frac{$8,000}{$116,000} = 4.07 \text{ years}\]
