Financial Management Notes

Financial Management Lecture Notes

Time Value of Money

The time value of money is a core principle of finance that states money available today is worth more than the same amount in the future due to its potential earning capacity. This concept assumes that money can earn interest, and therefore, any amount of money is worth more the sooner it is received.

Trial Question with Suggested Solution

Scenario: Investment Deal at Kunta Medical Centre
  • Initial Investment: GH¢500,000 over 3 years.
  • Interest Rate: 18% annual with quarterly compounding.

Terms of Proposed Investment Deal:

  1. Single Deposit:
    • GH¢500,000 deposited now with no additional payments.
    • Future Value (FV) can be calculated using the formula: FV = P \times (1 + r/n)^{nt} where:
      • P = 500,000
      • r = 0.18 (annual interest rate)
      • n = 4 (quarterly compounding)
      • t = 3 years.
  2. Multiple Deposits:
    • Initial deposit of GH¢500,000 with additional future deposits of GH¢50,000 at the start of year 2 and year 3.
    • Interest rates vary by year:
      • Year 1: 18%
      • Year 2: 18.5%
      • Year 3: 19%
i) Future Value Without Top-Up Deposits
  • To compute the future value with only the initial deposit:
    • Plugging values into the formula:
      FV = 500,000 \times (1 + 0.18/4)^{4 \times 3}
      FV = 500,000 \times (1 + 0.045)^{12}
      FV = 500,000 \times (1.045)^{12}
      FV \approx 500,000 \times 1.601032
      FV \approx GH¢800,516.00
ii) Future Value With Top-Up Deposits
  • Future value of initial deposit at the end of year 3:
    Using the previous calculation, it equals GH¢800,516.00.
  • Future value of the first top-up deposit of GH¢50,000:
    • Made at the beginning of Year 2:
      FV = 50,000 \times (1 + 0.185/4)^{4 \times 2}
      FV \approx 50,000 \times (1.04625)^{8}
      FV \approx 50,000 \times 1.3996 \approx GH¢69,980.00
  • Future value of the second top-up deposit of GH¢50,000:
    • Made at the beginning of Year 3:
      FV = 50,000 \times (1 + 0.19/4)^{4 \times 1}
      FV \approx 50,000 \times (1.0475)^{4}
      FV \approx 50,000 \times 1.1996 \approx GH¢59,980.00

Aggregate Future Value of All Deposits at End of Year 3:

  • Total Future Value = FV of initial deposit + FV of first top-up + FV of second top-up
  • Total Future Value = 800,516 + 69,980 + 59,980 = GH¢930,476.00

Class Discussion 11: Repayment of Loan

Scenario: Mrs. Alhassan’s Loan

  • Loan Amount: GH¢200 million.
  • Term: 4 years repayment with 1st payment due in 1 year.
  • Interest Rate: 5% over base rate of 23% p.a., totaling 28% p.a.
  • Repayment Structure: Equal payments for amortization of principal and interest calculated on a reducing balance.

Required:

a) Calculation of Annual Payments:
  • Use the formula for loan payments:
    P =\frac{L \cdot r (1+r)^n}{(1 + r)^n - 1}
  • Where:
    • L = 200,000,000 (loan amount)
    • r = 0.28
    • n = 4 (number of payments)

b) Amortization Schedule

  • The table will show the annual payments, interest on the outstanding principal, and the remaining balance after each payment. For a complete schedule, calculations need to be made year by year.

Class Discussion 12: Loan Application to Bank

Scenario: GH¢30,000 Loan Request

  • Loan Amount: GH¢30,000.
  • Term: 3 years repayment in equal installments.
  • Bank Policy: Maintain a maximum debt service ratio of 40% of this annual salary, which is GH¢12,000.
  • Interest Rate: 18% p.a.

Required:

a) Calculate Qualified Loan Size
  • Qualifying formula:
    P = \frac{A} {r}
    Rearranging for ability:
    P = 12,000 \times T \times (1 - (1 + 0.18)^{-n})\div (1 + 0.18)

b) Amortization Table

  • The amortization table shows the loan repayment breakdown including year, interest applied on the outstanding balance, and principal reductions.

Class Discussion 13: Equipment Financing

Scenario: Buhari Ltd. Purchase

  • Machine Cost: GH¢303,000.
  • Interest Rate: 12% p.a., repayable at the end of 4 years.
  • Sinking Fund Return Rate: 14% p.a.

Required:

a) Annual Payment into the Sinking Fund
  • Formula used:
    FV = C \cdot [(1+r)^t - 1]/r
    To find out the required contribution C to cover the loan principal and interest after 4 years.

b) Sinking Fund Schedule

  • A table with contributions, interest accrued, and balances until the loan is fully covered.