Forward rate $[10$ points$]$

Below is the treasury yield curve on $04/04/2025$ from Resource Center $|$ U$.$S$.$ Department of the Treasury

$\backslash$table$[[$Term$,6$ months,$1$ year,$2$ years,$3$ years,$5$ years,$7$ years,$10$ years,$20$ years,$30$ years$],[$Rate $(\%),4\mathrm{.}14,3\mathrm{.}86,3\mathrm{.}68,3\mathrm{.}66,3\mathrm{.}72,3\mathrm{.}84,4\mathrm{.}01,4\mathrm{.}44,4\mathrm{.}41]]$

a$.$ Your friend, Tony, plans to buy a car by taking out a $4-$year loan in $1$ year. He asks you if you know how to find the expected four$-$year rate, one year from now. Please help Tony calculate the forward rate. $[5$ points$]$

b$.$ You want to borrow a $1-$year $$10,000$ loan to start a business. You are not sure if you should borrow it today or wait a year to borrow. Find one$-$year interest rate, one year from today to compare oneyear rate today and one$-$year rate a year from now. $[5$ points$]$

$2.$ A semiannual coupon bond has a $$1,000$ par value, $20$ years to maturity, and a $5\%$ coupon rate and sells for $$1,070.$

a$.$ Find yield to maturity $($YTM$).$ Note: YTM must be an annual term as your final answer. $[5$ points$]$

b$.$ Assume that the yield to maturity remains constant for the next $11$ years. What will the price be $11$ years from today? $[5$ points$]$

$3.$ Dreamwork Co$.($DRC$)$ produces films for streaming companies. DRC is growing well and needs more capital to fund a new project. DRC plans to issue $12-$year bonds with $$1,000$ par value at the price of $$990.$ If DRC would like the cost of debt $($or yield to maturity$)$ to be no more than $4$ percent, what would be the coupon rate $(\%)$ for this bond to allow DRC to have the cost of debt of $4$ percent? $[5$ points$]$

$4.$ Risk and returns $[17$ points$]$

$\backslash$table$[[$Probability$,$Return of Stock A $(\%),$Return of Stock B $(\%)],[0\mathrm{.}4,-13,-20],[0\mathrm{.}5,5,3],[0\mathrm{.}1,18,25]]$

a$.$ Find expected return of Stock A and $B$ based on the probability. $[8$ points$]$

b$.$ Calculate expected return of the portfolio with $60\%$ investment in stock A and $40\%$ investment in stock B$.$ Hint: You will need to use answers from part a$)$ as part of your calculation $[3$ points$]$

c$.$ Calculate CAPM returns for stock C and D given that risk$-$free rate is $3$ percent and market risk premium is $4$ percent. Stock C$\text{'}$s beta is $1\mathrm{.}1$ and stock D$\text{'}$s beta is $0\mathrm{.}5.[6$ points$]$