$|$EC $202-$ Homework $4$

$-$ Wensleydale's bank has deposits of $\backslash (\backslash$$ $500\backslash$mathrm$\{$~m$\}\backslash ).$ It holds reserves of $\backslash (\backslash$$ $80\backslash$mathrm$\{$~m$\}\backslash ).$ It has purchased government bonds worth $\backslash (\backslash$$ $100\backslash$mathrm$\{$~m$\}\backslash ).$ It has made loans worth $\backslash (\backslash$$ $350\backslash$mathrm$\{$~m$\}\backslash ).$

$-$ Set up a T$-$account balance sheet for Wensleydale's Bank using the below table.

Wensleydale's Bank Balance Sheet

$-$ Calculate Wensleydale's bank's net worth.

$-$ Everard Bank is the only bank in the economy. The people in this economy have $\backslash (\backslash$$ $50\backslash )$ million in money, and they deposit all their money in Everard Bank.

$-$ Assume Everard Bank decides on a policy of holding $\backslash (100\backslash \%\backslash )$ reserves.

Draw a T$-$account for the bank.

Everard Bank's Balance Sheet

$-$ Now, assume Everard Bank is required to hold $\backslash (10\backslash \%\backslash )$ of its existing $\backslash (\backslash$$ $50\backslash )$ million as reserves, and to loan out the rest. Draw a T$-$account for the bank after this first round of loans has been made.

Everard Bank's Balance Sheet $-$ Now assume that Everard bank is part of a multibank system. Calculate by how much the money supply will increase given the reserve requirement and lending activity from part B$.$

$-$ If you buy a share of Apple stock today, assume the following is true: a$)$ you will be able to sell it in $3$ years for $\backslash (\backslash$$ $65\backslash )$ and b$)$ you will receive a $\backslash (\backslash$$ $5\backslash )$ dividend at the end of each of those three years.

$-$ If the prevailing interest rate is $\backslash (10\backslash \%\backslash ),$ what is the value of a share of Apple today?

$-$ If the present price is $\backslash (\backslash$$ $60\backslash ),$ should you buy the share?

$-$ Suppose a $5-$year bond with a $\backslash (\backslash$$ $50,000\backslash )$ face value pays $\backslash (10\backslash \%\backslash )$ annual coupon and has $2$ years left until maturity. The discount rate for this bond is $\backslash (5\backslash \%\backslash ).$ What is the net present value of the bond?