Question

1. Assuming that the pure rate of interest is 2%, and investors require an inflation premium of 3.5% and a risk premium of 6% to invest in a certain security, calculate the following rates using the multiplicative form of the Fisher model:

The nominal rate of interest on the security

The real rate of interest on the security

The risk-free rate of interest on securities of this maturity 

  (2 decimal places)

 

2.  An Inyo County California municipal bond is currently yielding 4.2%. What after-tax yield would you receive if you are in the following circumstances:

You are in a 28% federal tax bracket, and, as a California resident, you are in the 5% state tax bracket.

You are in a 33% federal tax bracket, and, as a Utah resident, you pay a 4% state income tax.

You are in a 15% federal tax bracket, and, as a Nevada resident, you pay no state income tax because Nevada has no income tax. 

 ( 2 decimal places.)

 

3. The expected return on a share of ExxonMobil stock in the U.S. is 15.6% while the expected return on a share of Royal Dutch Shell stock is 12.6% in the Netherlands. If the pure rate of return is 2% in both countries and the required risk premium is 6% for each company's stock, what is the long-term expected inflation rate in each country if the multiplicative form of the Fisher model is used in making the calculations?  

 (2 decimal places.) 

Answer 1

Part 1	Risk free rate of interest = ((1+pure interest) (1+inflation premium))-1
	Pure interest = 2%
	Inflation Premium = 3.5%
	Risk free rate of interest = ((1+2%)(1+3.5%))-1
	Risk free rate of interest = ((1.02)(1.035))-1
	Risk free rate of interest = 5.57%
	Nominal interest rate is the pure interest rate + inflation premium
	Nominal interest rate = 2% + 3.5%
	Nominal interest rate = 5.5%
	Fisher equation
	(1+nominal interest rate)= (1+ real interest rate) (1+inflation rate)
	Real interest rate = (1+nominal interest rate)/(1+inflation rate)-1
	Real interest rate = (1+nominal interest rate)/(1+inflation rate)-1
	Real interest rate = ((1+5.5%)/(1+3.5%))-1
	Real interest rate = (1.055/1.035)-1
	Real interest rate = 1.93%

Part 2	Bond Current Yield = 4.2%
a)	Federal tax = 28%
	State tax=5%
	Effective tax rate = 5%*(1-28%)+28%
	Effective tax rate = 3.6%+28%
	Effective tax rate = 31.6%
	After tax yield = Bond yield/(1-effective tax rate)
	After tax yield = 4.2/(1-31.6%)
	After tax yield = 4.2/(1-31.6%)
	After tax yield = 4.2/(1-31.6%)
	After tax yield = 4.2/0.684
	After tax yield = 6.14%
b)	Utah resident
	In this case we cant deduct the state tax payment in federal tax return
	After tax yield = Bond yield/(1-Federal tax rate- state tax rate)
	After tax yield = 4.2/(1-33%-4%)
	After tax yield = 4.2/0.63
	After tax yield = 6.67%
c)	There is only federal tax
	After tax yield = Bond yield/(1-Federal tax rate)
	After tax yield = 4.2/(1-15%)
	After tax yield = 4.2/0.85
	After tax yield = 4.9%