The Ghana Cocoa Board $($COCOBOD$)$ has, today, launched a debt securities exchange programme $($the Exchange Programme$)$ under which it is inviting holders of its short$-$term debt securities $($the Cocoa Bills$)$ to voluntarily offer to exchange their Cocoa Bills $($representing an aggregate principal of approximately GHS $7\mathrm{.}93$ billion$)$ for longer$-$term debt securities with averagely lower coupon rates to be issued by COCOBOD $($the Bonds$).$

Holders of the Cocoa Bills whose offers are accepted by COCOBOD will receive five $(5)$ different Bonds with an aggregate principal amount $($rounded down to the nearest GHS $1\mathrm{.}00)$ equal to the principal amount of Cocoa Bills tendered $($in addition to any accrued and unpaid interest due on such Cocoa Bills$).$ The five $(5)$ Bonds will mature on a one$-$per$-$year basis consecutively from $($and including$)2024$ to $($and including$)2028.$

i$)$ The short$-$term debt securities referred to mature in August $2023.$ If you were a current holder of a cocoa bill and you signed on to this arrangement, without a doubt, what would be the impact of this announcement on your financial position?

ii$)$ The Exchange Memorandum gives the following detail about the $5$ bonds to be received:

New Bond due $20242025202620272028$

$\%$ to be received $5\%20\%25\%25\%25\%$

ii$)$ If GHS $100,000$ were due to you in August $2023,$ but you accepted this proposal, calculate the present value of what you expect to receive. How much would you have gained or lost, $($Please indicate gain or loss$).$ Your opportunity cost is $32\%$ p$.$a$.$ Indicate any assumptions that you require.

iii$)$ The debt exchange is said to be optional. Suppose you did not sign on to this proposal, what is the likely outcome that you face?

a$)$ Risk and return

i$.$ What is the benefit of diversification of investment?

ii$.$ Will diversification lead to greater expected portfolio returns?

iii. Under what condition is portfolio risk reduction not possible?

Suppose project A has an expected return of $27\%$ and a standard deviation of $16\%$ while project B has an expected return of $21\%$ and a standard deviation of $12\%.$ Suppose Mr$.$ Just invested $2/3$ of his money in Project A and the remaining in Project B and that the correlation coefficient between the returns on the two projects is $0\mathrm{.}5.$

iv$)$ What are the expected return and standard deviations of Mr$.$ Just's portfolio?

v$)$ Is Mr$.$ Just's portfolio better or worse off than one invested entirely in project A$,$ or is it not possible to say?

b$)$ Treasury bill investments

Here's a summary of the Ghana Treasury bills auction held on July $14,2023$:

Security Discount Rate p$.$a$.$ "Interest" Rate p$.$a$.$

$91-$Day bill $23\mathrm{.}2515\%24\mathrm{.}6650\%$

$182-$Day bill $23\mathrm{.}3279\%26\mathrm{.}4082\%$

i$)$ What is the price of a $182-$Day bill that will pay you a total of GHS $100,000$ at maturity?

ii$)$ Unlike you, your friend wanted to receive GHS $100,000$ in $91$ days, so she bought the $91-$Day Treasury bill. She subsequently changed her mind and instructed her bank to "please rollover principal and interest." If interest rates remain the same, how much will your friend have in total after one year?

iii$)$ Calculate the effective annual rate that your friend would have earned!