Mini Case: 4 -37
or in part.
l. 2. What is the PV of the same stream?
Answer: 0 1 2 3
| | | | | | |
100 100 100
l. 3. Is the stream an annuity?
l. 4. An important rule is that you should never show a nominal rate on a time line or
use it in calculations unless what condition holds? (Hint: Think of annual
compounding, when INOM = EFF% = IPER.) What would be wrong with your
answer to questions l(1) and l(2) if you used the nominal rate (10%) rather than
the periodic rate (INOM /2 = 10%/2 = 5%)?
5%
Mini Case: 4 – 38
or in part.
m. Suppose someone offered to sell you a note calling for the payment of $1,000 15
months from today. They offer to sell it to you for $850. You have $850 in a
bank time deposit which pays a 6.76649% nominal rate with daily compounding,
which is a 7% effective annual interest rate, and you plan to leave the money in
the bank unless you buy the note. The note is not risky—you are sure it will be
paid on schedule. Should you buy the note? Check the decision in three ways:
(1) by comparing your future value if you buy the note versus leaving your
money in the bank, (2) by comparing the PV of the note with your current bank
account, and (3) by comparing the EFF% on the note versus that of the bank
account.
Answer: You can solve this problem in three ways—(1) by compounding the $850 now in the
bank for 15 months and comparing that FV with the $1,000 the note will pay, (2) by
finding the PV of the note and then comparing it with the $850 cost, and (3) finding
the effective annual rate of return on the note and comparing that rate with the 7%
you are now earning, which is your opportunity cost of capital. All three procedures
lead to the same conclusion. Here is the time line:
if you buy the note. (Again, you can find this value with a financial calculator.
Note that certain calculators like the hp 12c perform a straight-line interpolation
for values in a fractional time period analysis rather than an effective interest
rate interpolation. The value that the hp 12c calculates is $925.42.) This
procedure indicates that you should buy the note.
Alternatively, PV = $1000/(1.00018538)456 = $918.95.
Mini Case: 4 -39
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or in part.
(3) FVN = PV(1 + I)N, So $1,000 = $850(1 + i)1.25 = $1,000. Since we have an
equation with one unknown, we can solve it for i. You will get a value of i =
13.88%. The easy way is to plug values into your calculator. Since this return
is greater than your 7% opportunity cost, you should buy the note. This action
will raise the rate of return on your asset portfolio.
Alternatively, we could solve the following equation:
Web Extension 4C Continuous Compounding and Discounting
Solutions to Problems
4C-1 FV15 = $15,000e0.06(15) = $36,894.05.
Continuous compounding:
4C-4 Calculate the growth factor using PV and FV which are given:
Inputs: 2.0. Press LN key. Output: LN = 0.6931.
I(6)ln e = ln 2.0
I(6) = 0.6931
I = 0.1155 = 11.55%.
Web Extension 4C: 4 –41
or in part.
4C-7 e(0.03)(10) =
20
NOM
2
I
1
e0.3 =
20
NOM
2
I
1
INOM
2
2
INOM = 0.0302 = 3.02%.
Step 2: Calculate the PV or initial deposit: