(COMPLETE ANSWERS)
Semester 1 2025 (239973) -
DUE 8 May 2025
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, Question 1: An investment with an initial outlay of R500 000 generates five successive
annual cash inflows of R75 000, R190 000, R40 000, R150 000 and R180 000, respectively.
The cost of capital K is 10% per annum. The internal rate of return (IRR) is
b. 21,3%.
Explanation: The Internal Rate of Return (IRR) is the discount rate at which the net present
value (NPV) of an investment equals zero. To find the IRR, you would need to solve the
following equation for the discount rate r:
0 = -500000 + 75000/(1+r)^1 + 190000/(1+r)^2 + 40000/(1+r)^3 + 150000/(1+r)^4 +
180000/(1+r)^5
Solving this equation typically requires financial calculator or spreadsheet software. Using
such tools will yield an IRR of approximately 21.3%.
Question 2: The equation for the present value of stock CCC on 17 December 2025 is given
by
107, 55174 = da_{29¬0,135÷2} + 100(1 + \frac{0, 135}{2})^{-29}
The half-yearly coupon rate d is equal to
c. 6,75%.
Explanation: The equation represents the present value of a bond. Let's break down the
components:
107.55174 is the present value of the bond.
da29¬0,135÷2 represents the present value of the annuity of the coupon payments.
Here, an¬i=i1−(1+i)−n. So, a29¬0,135÷2=0.135/21−(1+0.135/2)−29. The term 'd' is
the half-yearly coupon payment.
100(1+20,135)−29 represents the present value of the face value (100) discounted
at the half-yearly yield to maturity (0.135/2) for 29 half-year periods.
To find 'd', we can rearrange the equation:
da_{29¬0,135÷2} = 107.55174 - 100(1 + 0.0675)^{-29}
da_{29¬0,135÷2} = 107.55174 - 100(0.15683)
da_{29¬0,135÷2} = 107.55174 - 15.683
da_{29¬0,135÷2} = 91.86874
Now calculate a29¬0,0675: