Your client Small and Bold, a leading microfinance entity, is considering developing a new five$-$year fund SBOLD to expand operations across the world. SBOLDs sources of funding include:

Commercial investors who demand security and high rates of return

Sub$-$commercial investors who like security and are willing to accept lower rates of

return because they believe in Small and Bolds mission

Small and Bolds funds

The terms for SBOLDs investors are in the table below.

Investor Type Yearly Interest Size of Investment

Commercial $8\%50$m

Sub$-$commercial $6\%20$m

Small and Bold $5\%5$m

The investments in SBOLD are expected to grow by some figure between $-26\%$ and $44\%$ each

year $-$ this return can vary from year to year $($it need not be the same all five years$)$ and will be

randomly, evenly $($uniformly$)$ distributed between $-26\%$ and $44\%.$

Interest is paid every year at the end of the year to each investor group according to the interest

rate and initial size of the investment $($shown above$).$ The interest is paid out of the investments and

the remaining funds stay invested for next year. So for example, if at the beginning of the year,

$$80$m was invested, the return for that year was $10\%,$ and interest of $$7$ million was owed for the

year, SBOLD would have $$80$ x $(1+10\%)-$ $$7=$ $$81$ million in investments at the end of the

year.

The principal $($which corresponds to the size of the initial investment$)$ will be paid back at the

end of $5$ years if there are sufficient funds available. At the end of time $5,$ the Commercial

Investors get paid their principal first, the Sub$-$commercial Investors get paid their principal

second, and Small and Bold gets whatever is left over after paying these investors.

a$.$ What are the amounts that Commercial Investors, Sub$-$Commercial Investors, and Small

and Bold expect to get paid back in principal $($assume they get paid all of their promised

interest all $5$ years$)?$ Please run at least $5,000$ observations and calculate the average.

b$.$ How often do our Commercial and Sub$-$Commercial investors get paid back in full?

c$.$ Sub$-$commercial investors are concerned that they are taking too much risk for the

return they receive. These investors would like to receive a share of the profits after

Small and Bold get paid back their investment of $$5$m in year $5.$ What percentage of the

SBOLDs profits should the Sub$-$commercial investors demand so they are expected to

average getting back $$20$ million in principal at year $5($this $$20$ million is in addition to

all of the interest they receive$)?$