money and time value

The time value of capital is a financial accounting philosophy that claims that “money available today is worth more than the same amount in the future due to its possible earning capacity” (Erdogdu, Arun & Ahmad, 2016, p. 351). This essentially means that money earned in the future has less value than money received in the present.
Future Value: Mankiw, Croushore & Stull (2009, p. 578) define future value as “the amount of money in the future that an amount of money today will yield, given prevailing interest rates.
The formula for calculating future value is C0 * (1+r) ^n whereby:
(i) C0 is the cash flow at period 0,
(ii) R is the rate of return, and
(iii) N is the number of periods
This formula of future value is used to work out the value of cash flows after a certain period of time, as compared to when money was received. The time value of money concept posits that money at hand does not have the same value as money to be received at a later date.
Present Value: this is defined as “the amount you would pay now for an amount to be received ‘n’ periods in the future given an interest rate of ‘i’” (Delaney & Whittington, 2009, p. 336). The present value of ‘x’ amount of money is the inverse of the future value of that same amount of money (Moyer, McGuigan & Rao, 2007).
The formula for calculating present value is PV= F V/ ((1+r) ^n) whereby:
(i) PV is the present value,
(ii) FV is the future value,
(iii) R is the rate of return, and
(iv) N is the number of periods
Solution to case no 1
In this case, an amount of 100, 000 dollars is invested over a 10 year period but at different rates, starting from 2%, 5%, 8% and finally, 10%. Due to the different rate of returns, it is expected that the future value of the amount will be change in each of the scenarios. The time period with the highest rate of return results in a higher compounded value of an investment as compared to the time period with the lowest rate of return. This is because when the rate is high, the returns are higher which also leads to an increase in the value of the investment in future.
Initial value \$100,000
Time period 10
Annual interest rate Future value of \$100, 000 after then years

From the above results, it can be deduced that the compound value of an investment increases with an increase in the annual interest rate. (Given the initial value of investment and time period remain the same).

Solution to case no 2
This question requires one to work out the present value of an investment that has varying cash flows for different time periods. The option with the highest or a value that is positive should be the most preferred because it provides greater value when compared to the other options that have the lowest or negative net present value. This case only provides cash inflows and therefore the present value of the project can be determined by multiplying the cash flows with the discount rate.
Discount rate 8%
Year Cash flow Present value of stream of cash flow
7
8
9
10 \$100,000
\$100,000
\$100,000
\$100,000
\$100,000 \$63,016.96
\$58,349.04
\$54,026.89
\$50.024.90
\$46,319.35
Net present value of cash flow streams \$900,790. 45

Looking at options (A and F), (B and E), and (C and D) it can be concluded that the present value of cash flow streams decreases with an increase in time period. (Given that the future value of cash flow and discount rate remain the same).
Solution case no 3
This case requires one to apply different discount rates for different years. The present value factor will, therefore, be different from the previous case because it is determined by the discount rate applied, which varies for the different years.

Year Discount rate Cash flow Present value of stream of cash flow
Answer A 1 8% \$100,000 \$92,592.59
Answer B 2 6% \$150,000 \$133,499.47
Answer C 3 10% \$200,000 \$150,262.96
Answer D 4 4% \$200,000 \$170,960.84
Answer E 5 6% \$150,000 \$112,088.73
7
8
9
10 4%
4%
4%
4%
4% \$100,000
\$100,000
\$100,000
\$100,000
\$100,000 \$79,031.45
\$75,991.78
\$73,069.02
\$70,258.67
\$67,556.42
Net present value of cash flow streams \$1,025,311.93
From the results of answer F, it can be concluded that the present value of stream of cash flow decreases with an increase in the time period. (Given the future value of cash flow and discount rates remain the same).

References
Delaney, P., & Whittington, R. (2009). Wiley CPA exam review 2010. Hoboken, N.J.: Wiley.
Erdogdu, M., Arun, T., & Ahmad, I. (2016). Handbook of research on green economic development initiatives and strategies. Hershey: IGI Global.
Mankiw, N., Croushore, D., & Stull, C. (2009). Principles of economics. Fort Worth [u.a.]: Dryden Pr.
Moyer, R., McGuigan, J., & Rao, R. (2007). Fundamentals of contemporary financial management. Eagan, MN: Thomson/South-Western.