# What is the role of return and risk in financial decisions?

What is the role of return and risk in financial decisions? The purpose of this assignment is to solidify your understanding of the applications of the risk

and return concepts and their role in valuing financial assets. The scores of this assignment will

help in assessing the following learning goal of the course: “students successfully completing

this course will be able to Analyze risk-return characteristics to assess the valuation of financial

assets”.

and return concepts and their role in valuing financial assets. The scores of this assignment will

help in assessing the following learning goal of the course: “students successfully completing

this course will be able to Analyze risk-return characteristics to assess the valuation of financial

assets”.

## Why the concept of risk and return is an important aspect of finance?

Instructions:

You are required to use a financial calculator or spreadsheet related to the risk and return stocks, and bonds valuation. You are required

to show the following 3 steps for each problem (sample questions and solutions are provided for

guidance):

(i) Describe and interpret the assumptions related to the problem.

(ii) Apply the appropriate mathematical model to solve the problem.

(iii) Calculate the correct solution to the problem.

Sample Questions and Solutions

Sample Question # 1:

A company has an issue of 12-year bonds that pay 5% interest, annually. Further, assume that

today’s required rate of return on these bonds is 7%. How much would these bonds sell for

today? Round off to the nearest $1.

You are required to use a financial calculator or spreadsheet related to the risk and return stocks, and bonds valuation. You are required

to show the following 3 steps for each problem (sample questions and solutions are provided for

guidance):

(i) Describe and interpret the assumptions related to the problem.

(ii) Apply the appropriate mathematical model to solve the problem.

(iii) Calculate the correct solution to the problem.

Sample Questions and Solutions

Sample Question # 1:

A company has an issue of 12-year bonds that pay 5% interest, annually. Further, assume that

today’s required rate of return on these bonds is 7%. How much would these bonds sell for

today? Round off to the nearest $1.

### What is the relationship between risk and return in financial management?

Solution

(i) The problem assumes that the face value of the bond is $1000. The bond will pay an

annual coupon of 5% i.e., coupon or interest amount of $50 is assumed to paid every

year. It also assumes that investors currently required a return of 7% on investments

with similar risk characteristics. The use of bond valuation concept is appropriate to

calculate the true value of these bonds. The accuracy of the solution depends on the

correctness of the assumptions on face value, coupon payments, and required rate of

return assumption.

(ii) The use of the bond valuation concept which suggests that the true value of a bond is the

present value of its future coupon and face value discounted at investors’ required rate

of return is appropriate to calculate the true value of these bonds. We are required to

compute the present value (PV) which represents the true value of the bond.

(iii) FV= $1000; PMT=$50; Rate = 7%; N=12 years; Compute PV = ? = $841.15

Value of the Bond = $841.15

(i) The problem assumes that the face value of the bond is $1000. The bond will pay an

annual coupon of 5% i.e., coupon or interest amount of $50 is assumed to paid every

year. It also assumes that investors currently required a return of 7% on investments

with similar risk characteristics. The use of bond valuation concept is appropriate to

calculate the true value of these bonds. The accuracy of the solution depends on the

correctness of the assumptions on face value, coupon payments, and required rate of

return assumption.

(ii) The use of the bond valuation concept which suggests that the true value of a bond is the

present value of its future coupon and face value discounted at investors’ required rate

of return is appropriate to calculate the true value of these bonds. We are required to

compute the present value (PV) which represents the true value of the bond.

(iii) FV= $1000; PMT=$50; Rate = 7%; N=12 years; Compute PV = ? = $841.15

Value of the Bond = $841.15

#### What is the difference between risk and return?

2

Sample Question # 2:

A company just paid a dividend of $1, and the dividends are expected to grow at a constant rate of

4% forever. If the required return of the stockholders is 12%, what is the price of this company’s

stock?

Solution

(i) The problem assumes the stock will have a constant growth of 4% forever. The

constant growth model is appropriate to use for this problem. The accuracy of the

solution depends on the correctness of the constant growth assumption.

(ii) The constant growth model is given as: P0 = D1/ (R-g); where

• P0 is the current price to be calculated,

• D1 is the next period’s dividend,

• R is the required return on this stock

• g is the constant growth

D1 needs to be calculated in order to apply this model.

(iii) D1= $1.00 x (1+0.04) = 1.04

P0 = 1.04/(0.12-0.04) = $13;

the stock price should be $13 based on the constant growth model.

Sample Question # 2:

A company just paid a dividend of $1, and the dividends are expected to grow at a constant rate of

4% forever. If the required return of the stockholders is 12%, what is the price of this company’s

stock?

Solution

(i) The problem assumes the stock will have a constant growth of 4% forever. The

constant growth model is appropriate to use for this problem. The accuracy of the

solution depends on the correctness of the constant growth assumption.

(ii) The constant growth model is given as: P0 = D1/ (R-g); where

• P0 is the current price to be calculated,

• D1 is the next period’s dividend,

• R is the required return on this stock

• g is the constant growth

D1 needs to be calculated in order to apply this model.

(iii) D1= $1.00 x (1+0.04) = 1.04

P0 = 1.04/(0.12-0.04) = $13;

the stock price should be $13 based on the constant growth model.