I. Calculate the weighted average cost of capital (WACC) for M Co as at 31 December 2018. ii. Briefly advise the directors of M Co on the suitability of using the WACC calculated in (a) above to discount the expected cash flows of the project.

The cost of equity is calculated using the Dividend Growth Model ($K_e = \frac{D_1}{P_0} + g$).

• Current market price per share ($P_0$) = GH¢1.45.
• Most recent dividend ($D_0$) = 14.1 cents = GH¢0.141.
• Calculate the dividend growth rate ($g$) using the geometric mean from 2014 to 2018: $$g = \left(\frac{D_{2018}}{D_{2014}}\right)^{\frac{1}{n}} - 1 = \left(\frac{0.141}{0.110}\right)^{\frac{1}{4}} - 1$$ $$g = (1.281818)^{\frac{1}{4}} - 1 = 1.0639 - 1 = 0.0639 \text{ or } 6.39\%$$
• Next year's dividend ($D_1$) = $D_0 (1+g) = GH¢0.141 \times (1 + 0.0639) = GH¢0.141 \times 1.0639 = GH¢0.1509$.
• Cost of Equity ($K_e$): $$K_e = \frac{GH¢0.1509}{GH¢1.45} + 0.0639 = 0.104069 + 0.0639 = 0.167969 \text{ or } 16.80\%$$

• Number of shares = 3 million.
• Market price per share = GH¢1.45. $$V_e = 3,000,000 \times GH¢1.45 = GH¢4,350,000$$

• Debentures:
  • Nominal value = GH¢1,000,000.
  • Coupon rate = 7%.
  • Redemption value = GH¢100 per GH¢100 nominal.
  • Current market price = GH¢83.60 per GH¢100 nominal.
  • Years to maturity ($N$) = $2022 - 2018 = 4$ years.
  • Annual interest payment ($I$) = 7% of GH¢100 = GH¢7.
  • Pre-tax cost of debentures ($K_{d,deb}$) is calculated using interpolation for Yield to Maturity (YTM):
    • At 12%: $7 \times PVAF(12\%, 4) + 100 \times PVF(12\%, 4) = 7 \times 3.0373 + 100 \times 0.6355 = 21.2611 + 63.55 = 84.8111$
    • At 13%: $7 \times PVAF(13\%, 4) + 100 \times PVF(13\%, 4) = 7 \times 2.9745 + 100 \times 0.6133 = 20.8215 + 61.33 = 82.1515$
    • $K_{d,deb} = 12\% + (13\% - 12\%) \times \frac{84.8111 - 83.60}{84.8111 - 82.1515} = 12\% + 1\% \times \frac{1.2111}{2.6596} = 12\% + 0.4553\% = 12.46\%$
  • Market value of debentures ($V_{d,deb}$) = $\frac{GH¢1,000,000}{GH¢100} \times GH¢83.60 = GH¢836,000$.
• Bank Loan:
  • Amount = GH¢500,000.
  • Interest rate = 8%.
  • Pre-tax cost of bank loan ($K_{d,loan}$) = $8\%$.
  • Market value of bank loan ($V_{d,loan}$) = GH¢500,000.
• Total Market Value of Debt ($V_d$): $$V_d = V_{d,deb} + V_{d,loan} = GH¢836,000 + GH¢500,000 = GH¢1,336,000$$

• After-tax cost of debentures = $K_{d,deb}(1-T) = 0.1246 \times (1 - 0.30) = 0.1246 \times 0.70 = 0.08722 \text{ or } 8.72\%$.
• After-tax cost of bank loan = $K_{d,loan}(1-T) = 0.08 \times (1 - 0.30) = 0.08 \times 0.70 = 0.056 \text{ or } 5.60\%$.

• Total market value of capital ($V$) = $V_e + V_d = GH¢4,350,000 + GH¢1,336,000 = GH¢5,686,000$.
• WACC formula: $WACC = K_e \left(\frac{V_e}{V}\right) + K_{d,deb}(1-T) \left(\frac{V_{d,deb}}{V}\right) + K_{d,loan}(1-T) \left(\frac{V_{d,loan}}{V}\right)$ $$WACC = 0.1680 \left(\frac{4,350,000}{5,686,000}\right) + 0.08722 \left(\frac{836,000}{5,686,000}\right) + 0.056 \left(\frac{500,000}{5,686,000}\right)$$ $$WACC = 0.1680 \times 0.76504 + 0.08722 \times 0.14703 + 0.056 \times 0.08793$$ $$WACC = 0.12852672 + 0.0128289 + 0.00492408$$ WACC = 0.1462797 \text{ or } \boxed{\text{14.63%}}