a) Syndicated loan
i) Computation of the loan’s balance at the end of the moratorium

FVn=P0(1+im)mnFVn=GH5̸0,000,000(1+0.284)2×4=GH8̸5,909,309\begin{gathered} \mathrm{FV}_{\mathrm{n}} = \mathrm{P}_0 \left(1 + \frac{\mathrm{i}}{\mathrm{m}}\right)^{\mathrm{mn}} \\ \mathrm{FV}_{\mathrm{n}} = \mathrm{GH} \not 50,000,000 \left(1 + \frac{0.28}{4}\right)^{2 \times 4} = \mathrm{GH} \not 85,909,309 \end{gathered}FVn​=P0​(1+mi​)mnFVn​=GH50,000,000(1+40.28​)2×4=GH85,909,309​

(3 marks)

ii) Computation of the quarterly instalment required to amortise the loan over ten years.

PVA=PMT[1−1(1+im)n⋅mim]GH8̸5,909,309=PMT[1−1(1+0.284)10⋅40.284]PMT=GH8̸5,909,30913.33170884=GH6̸,443,983.29\begin{aligned} & \text{PVA} = \text{PMT} \left[ \frac{1 – \frac{1}{\left(1 + \frac{\mathrm{i}}{\mathrm{m}}\right)^{\mathrm{n} \cdot \mathrm{m}}}}{\frac{\mathrm{i}}{\mathrm{m}}} \right] \\ & \text{GH} \not 85,909,309 = \text{PMT} \left[ \frac{1 – \frac{1}{\left(1 + \frac{0.28}{4}\right)^{10 \cdot 4}}}{\frac{0.28}{4}} \right] \\ & \text{PMT} = \frac{\text{GH} \not 85,909,309}{13.33170884} = \text{GH} \not 6,443,983.29 \end{aligned}​PVA=PMT​mi​1−(1+mi​)n⋅m1​​​GH85,909,309=PMT​40.28​1−(1+40.28​)10⋅41​​​PMT=13.33170884GH85,909,309​=GH6,443,983.29​

The university must pay GH¢6,443,983.29 every quarter to settle the loan over the 10-year repayment period.
(4 marks)

b) Bond issue
i) Computation of the total redemption value of the bond.

Redemption price=GH1̸,000×(1+0.1)=GH1̸,100Total RV=50,200×GH1̸,100=GH5̸5,220,000\begin{gathered} \text{Redemption price} = \mathrm{GH} \not 1,000 \times (1 + 0.1) = \mathrm{GH} \not 1,100 \\ \text{Total RV} = 50,200 \times \mathrm{GH} \not 1,100 = \text{GH} \not 55,220,000 \end{gathered}Redemption price=GH1,000×(1+0.1)=GH1,100Total RV=50,200×GH1,100=GH55,220,000​

(3 marks)

ii) The size of each semi-annual instalment into the sinking fund.

FVADn=PMT[(1+im)n⋅m−1im](1+im)55,220,000=PMT[(1+0.202)13×2−10.202](1+0.202)PMT=GH5̸5,220,000120.0999419=GH4̸59,783.74\begin{gathered} \text{FVAD}_{\mathrm{n}} = \text{PMT} \left[ \frac{\left(1 + \frac{\mathrm{i}}{\mathrm{m}}\right)^{\mathrm{n} \cdot \mathrm{m}} – 1}{\frac{\mathrm{i}}{\mathrm{m}}} \right] \left(1 + \frac{\mathrm{i}}{\mathrm{m}}\right) \\ 55,220,000 = \text{PMT} \left[ \frac{\left(1 + \frac{0.20}{2}\right)^{13 \times 2} – 1}{\frac{0.20}{2}} \right] \left(1 + \frac{0.20}{2}\right) \\ \text{PMT} = \frac{\text{GH} \not 55,220,000}{120.0999419} = \text{GH} \not 459,783.74 \end{gathered}FVADn​=PMT[mi​(1+mi​)n⋅m−1​](1+mi​)55,220,000=PMT[20.20​(1+20.20​)13×2−1​](1+20.20​)PMT=120.0999419GH55,220,000​=GH459,783.74​

(4 marks)

c) Computation of the project’s NPV and investment recommendation

Workings:

Terminal value5=NCF5(1+g)r−g=20(1+10%)0.30−0.10=110\text{Terminal value}_5 = \frac{\text{NCF}_5 (1 + \mathrm{g})}{\mathrm{r} – \mathrm{g}} = \frac{20 (1 + 10\%)}{0.30 – 0.10} = 110Terminal value5​=r−gNCF5​(1+g)​=0.30−0.1020(1+10%)​=110

Investment recommendation:
The project should be accepted for implementation. The positive NPV suggests that the project will increase the value of the university when implemented.
(6 marks)
(Total: 20 marks)

EXAMINER’S COMMENTS
Question Two posed a lot of challenges to most candidates as reflected in the pass rate. Candidates were tested on computation of outstanding loans values and redemption values of bonds and the size of semi-annual instalment into a sinking fund for redemption to redeem the debt. Understanding the right formulas to use and how to compute was a major challenge to most candidates.
The overall pass rate was 12% compared to the 34% pass rate in the previous sitting and requires more focus by future candidates in this area to avoid reoccurrence. It was the worst answered question in the paper. Only 68 candidates obtained a pass or better in the question compared to 223 candidates in the previous sitting.