Answer 1)
Time Value of Money is an important concept in the world of finance. As per the principle, the value of money received today is more than the same amount of money to be received in some future date. In other words, as per the principle of Time Value of Money, money carries the power to earn interest. Thus, any amount of money is worth more the sooner it is received. For Instance, $100 invested at 10% rate of interest for 1 year will be $110 after the end of year. Similarly, if $100 is received after 1 year, this will presently valued at 100/1.10= $90.90. Hence, everyone will always prefer to receive money today rather than an year later as the amount received today can earn interest of one year.
Answer 2)
It is significantly important for the finance managers to understand the concept of the Time Value of Money, as this principle of finance can help in profitable structuring of their financial decisions. Since most of the finance managers relies on project appraisal decisions, their decision to accept or reject the project is dependant on Capital Budgeting technique, which itself is the by-product of Time Value of Money. Following techniques of Capital Budgeting, which is used by the financial managers, cannot be completed without understanding the TVM theory and application:
Net Present Value:
Any project being considered in the company is decided upon NPV value of the cash flows. However, the NPV method uses the concept of the time value of money to determine if the project is profitable or not. Thus, only after understanding TVM theories and applications, the finance managers, carry out NPV analysis of the related cash flows. Finally, if the NPV of the project is positive, the project is accepted else withdrawn. Hence, if the finance managers do not use the time value of money concepts, the projects with a long time horizon or in periods of high discount rate can be mispriced and an unprofitable decision could be made by the managers.
Comparing Investments:
Time Value of Money is not only useful in making capital budgeting decisions but it also guide the managers as where to invest their retained earnings. The Finance Managers compare the future value of two investment options and the investment with high future value is accepted, assuming both the investment product carry similar level of risk.
Answer 3)
FV= PV(1+r)n
Here, FV= Future Value
PV= Present Value
R= Interest Rate/ Compunding Period
N= Number of Compounding Periods till maturity
a.$150,537.19 if invested for seven years at a 5% interest rate:
FV= PV(1+r)n
FV= 150537.19(1+.05)7
FV= $211821
Hence, Future value of the amount invested after 7 years will be $211821.
b.$237,891.22 if invested for eight years at a 3% interest rate:
FV= PV(1+r)n
FV= 237891.22(1+.03)8
FV= $301353
Hence, Future Value of the amount invested after 8 years will be $301353.
c.$320,891.12 if invested for 10 years at an 11% interest rate:
FV= PV(1+r)n
FV= 320891.12(1+.11)10
FV= $911145
Hence, Future Value of the amount invested after 10 years will be $911145.
d.$520,520.22 if invested for 13 years with a 13% interest rate:
FV= PV(1+r)n
FV= 520520.22(1+.13)13
FV= $2549513
Hence, Future Value of the amount invested after 13 years will be $2549513.
Answer 4)
PV= FV/(1+r)n
Here, FV= Future Value
PV= Present Value
R= Interest Rate/ Compunding Period
N= Number of Compounding Periods till maturity
a.$562,126.17 to be received seven years from now with a 5% interest rate:
PV= FV/(1+r)n
PV= 562126.17/(1+.05)7
PV= 562126.17/ 1.40
PV= $399492.57
Hence, Present Value of the amount to be received after 7 years will be $399492.57
b.$225,003.21 to be received six years from now with a 6% interest rate:
PV= FV/(1+r)n
PV= 225003.21/ (1+.06)6
PV= 225003.21/1.418
PV= $158618.38
Hence, Present Value of the amount to be received after 6 years will be $158618.38
c.$321,567.35 to received five years from now with an 18% interest rate:
PV= FV/(1+r)n
PV= 321567.35/ (1+.18)5
PV= 321567.35/ 2.287
PV= $140560
Hence, Present Value of the amount to be received after 6 years will be $158618.38
d.$63,000.05 to be received twelve years from now with a 5% interest rate:
PV= FV/(1+r)n
PV= 63000.05/(1+.05)12
PV= 63000.05/ 1.795
PV= $35080.78
Hence, Present Value of the amount to be received after 6 years will be $158618.38
Answer 5)
Since, payments will be received at the end of each year, this is an ordinary annuity.
Present Value of Annuity= Payment per period[((1+r)n-1)/ (r(1+r)n)]
Payment per Period= $325,891.12
N= 12 years
R= 6%
Hence, Present Value of Annuity= 325891.12[((1+.06)12-1/.06(1+.06)12)]
PVA= 325891.12[(2.0122-1)/ 0.12073]
PVA= 325691.12(8.3841)
PVA=$2730620.80
Note: Using Financial Calculator, the answer will be: $2730544
Answer 6)
Future Value of an Annuity: Payment per period[((1+r)n-1)/ r]
Here, Payments per period= $ 437,891.24
R= 15%
N= 5 years
FV of Annuity= 437891.24[((1+.15)5-1)/ .15]
FV= 437891.24[(2.01136-1)/.15]
FV= 437891.24[6.7423]
FV= $2952429.86
Hence, depositing $437891.24 for eevry 5 years at 15% ROI will give us $2952429.86
Works Cited
Freedman, J. (n.d.). Why Is the Time Value of Money So Important in Capital Budgeting Decisions? Retrieved from azcentral.com: http://yourbusiness.azcentral.com/time-value-money-important-capital-budgeting-decisions-12009.html
Investopedia. (2014, March 1). Time Value of Money. Retrieved from Investopedia: http://www.investopedia.com/terms/t/timevalueofmoney.asp
Investopedia. (n.d.). Annuity. Retrieved from Investopedia: http://www.investopedia.com/terms/a/annuity.asp
O'Connor. (2011). Discounted Cash Flow Applications. In C. Institute, Quantitative Methods (pp. 138-150). Boston: Custom.
O'Connor. (2011). The Time Value of Money. In C. Institute, Quantitative Methods (pp. 195-199). Boston: Custom.
Time Value of Money: Why it is important? (n.d.). Retrieved from Boundless.com: https://www.boundless.com/finance/the-time-value-of-money/introduction-to-the-time-value-of-money/why-is-it-important--2/
