# What is an opportunity cost rate by jennyyingdi

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```									(2-2) What is an opportunity cost rate? How is this rate used in discounted cash flow
analysis, and where is it shown on the time line? Is the opportunity rate a single number
that is used in all situations?

Ans:
opportunity cost is the rate of return expected if an alternative course of action were
taken. The opportunity cost of investing in, say, a new business computer, could be the
interest that would have been earned had the computer’s purchase price been used to
purchase high grade bonds or some investment fetching return on investment.

Opportunity cost rate - is the rate of return one could earn on an alternative investment of
similar risk.

Opportunity cost rate is used to discount cash flows to arrive at one interest cost which
either is the borrowing cost or the cost foregone by inputting money somewhere else.
Example on timeline for opportunity cost rate is say
Year Investment         Inflow
0        \$ 10000        0
1        0              \$ 1500
2        0              \$ 2500
3        0              \$ 4000
Total \$ 10000           \$ 10000
Means the investment will fetch in \$ 10000 investment in 3 years time, however the time
value of money over 3 years will not be the same due to interest factor (cost) or the
inflation / depletion in time value.
Revision then comes at, say 10% or 15% (hypothetical) cost
Year Investment         Inflow         Present value
0        \$ 10000        0              discounted at say 10-15%
1        0              \$ 1500         say     \$ 1000
2        0              \$ 2500                 \$ 1800
3        0              \$ 4000                 \$ 3200

Total \$ 10000          \$ 10000                \$ 6000

Opportunity rate cannot be a single number used in all situations, it changes basis cost of
capital or the opportunity foregone or on the basis of number of years.

(2-3) An annuity is defined as a series of payments of a fixed amount for a specific
number of periods. Thus, \$100 a year for 10 years is an annuity, but \$100 in Year 1,
\$200 in Year 2, and \$400 in years 3 through 10 does not constitute an annuity. However,
the second series contains an annuity. Is this statement true or false? Explain.

Ans:

The term annuity is used in finance theory to refer to any terminating stream of fixed
payments over a specified period of time. This usage is most commonly seen in finance,
usually in connection with the valuation of the stream of payments, taking into account
time value of money concepts such as interest rate and future value.

Examples of annuities are regular deposits to a savings account, monthly home mortgage
payments and monthly insurance payments. Annuities are classified by payment dates.
The payments (deposits) may be made weekly, monthly, quarterly, yearly, or at any other
interval of time.

So in the above example first one of \$ 100 yearly is surely the case of Annuity, the
second one is also Annuity since this honours monthly/yearly payout, period payment
and is part of series of payments. The only difference in second one is that amount has
changed which does not alter the nature of annuity.

(2-4) If a firm’s earnings per share grew from \$1 to \$2 over a 10-year period, the total
growth would be 100%, but the annual growth rate would be less than 10%. True or
false? Explain.

Ans: True, the annual growth rate would be less than 10%

Growth of \$ 1 to \$ 2 over 10 year period does not mean annual growth of 10% because in
the case of annual 10% growth amount becomes \$ 2.36 as shown in following table.
Growth
Year     Earnings     %
1         \$1.00      10%
2         \$1.10
3         \$1.21
4         \$1.33
5         \$1.46
6         \$1.61
7         \$1.77
8         \$1.95
9         \$2.14
10         \$2.36

Whereas if growth rate of 8% annually is there, it makes the earnings of 1\$ to \$ 2
Growth
Year     Earnings     %
1         \$1.00       8%
2         \$1.08
3         \$1.17
4         \$1.26
5         \$1.36
6         \$1.47
7         \$1.59
8         \$1.71
9         \$1.85
10         \$2.00
(2-5)Would you rather have a savings account that pays 5% interest compounded semi-
annually or one that pays 5% interest compounded daily? Explain.

Ans: Interest conceptually is always more if it gets compounded at earlier frequency. In
the above case since the interest rate is same at 5%, so compounding it on a daily basis
would be more beneficial than compounding this on semi-annual basis (i.e once in 6
months). Explained in the following example:
Case A - Compounding semiannually          Case B - Compounding daily

Interest        Corpus      Day                Interest    Corpus
Month 6        \$1,000      \$25.00        \$1,025.00     1       \$1,000    \$0.1370   \$1,000.14
Month
12          \$1,025.00      \$25.63        \$1,050.63     2    \$1,000.14   \$0.1370    \$1,000.27
\$50.63                      3    \$1,000.27   \$0.1370    \$1,000.41
4    \$1,000.41   \$0.1370    \$1,000.55
Total interest becomes 50.61                 5    \$1,000.55   \$0.1371    \$1,000.69
6    \$1,000.69   \$0.1371    \$1,000.82
7    \$1,000.82   \$0.1371    \$1,000.96
137    \$1,018.80   \$0.1396    \$1,018.94
138    \$1,018.94   \$0.1396    \$1,019.08
139    \$1,019.08   \$0.1396    \$1,019.22
218    \$1,030.17   \$0.1411    \$1,030.31
219    \$1,030.31   \$0.1411    \$1,030.45
220    \$1,030.45   \$0.1412    \$1,030.59
299    \$1,041.66   \$0.1427    \$1,041.81
300    \$1,041.81   \$0.1427    \$1,041.95
363    \$1,050.84   \$0.1440    \$1,050.98
364    \$1,050.98   \$0.1440    \$1,051.12
365    \$1,051.12   \$0.1440    \$1,051.27
\$51.27

(Excel workings enclosed)
rs

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