Comprehensive Finance Assignment: Valuation, NPV, and Annuities

This document provides detailed solutions to a finance assignment, covering a range of financial concepts. The assignment begins with an analysis of shareholder wealth maximization, explaining its long-term strategy and drivers. It then differentiates between nominal and compounding period interest rates. The core of the assignment involves solving investment problems using Net Present Value (NPV) calculations, determining the viability of projects based on positive NPV values. The solution further explores investment types like perpetuities and uneven cash flows, calculating their present values. Additionally, the assignment delves into future value calculations for monthly payments and compares investment strategies, such as an ETF fund versus monthly retirement income, to assess financial sustainability. Finally, it calculates loan present values and contrasts nominal and effective interest rates, along with compounding period rates, emphasizing the importance of aligning payment and compounding periods for accurate financial computations. The student can use this document to understand financial concepts.

Question 1 Solutions
Part a
Creating shareholder wealth is a long term strategy which aims to increase a company’s share
price through multiple drivers like revenue, cost of capital, investment in working Capital etc. If
done correctly, maximizing a company’s assets can generate sales which can lead to increased
values. Hence, this strategy is consistent with the goals of maximizing shareholder wealth.
Part b- Differences
The difference between the two rates is as follows:
 Compounding period interest rate takes into account compounding, whereas the nominal
interest rate does not factor compounding
 The compounding period rate is stated as per the compounding period, whereas nominal
interest rate can be stated for any period: Annually, semiannually, quarterly, monthly,
weekly, daily, etc.
The compounding period rate is equal to nominal rate divided by number of compounding
periods
Question 2 Solutions
Solution a
In order to evaluate this project we need to calculate the Net Present Value (NPV). If NPV>0,
then it is a good investment
Information provided:
 Nominal rate=12% p.a compounded monthly
 t0=-30,000
 t2= 20,000
 t5=30,000
 i=effective interest rate= (1+ 0.12
12 )
12
-1
NPV= -30,000+ 20000∗(1+i)−2+30,000*(1+i)−5

Steps on Calculator
o To determine effective interest rate, enter nominal rate 12 press Nom %
o Enter compounding period 12, press P/YR
o Press shift ,EFF% to solve effective interest rate
o Store Interest rate
o Input the cash flows for (0,2&5) using CF and N
o Press the NPV key to solve
=$2,264
Since NPV> 0, then it is a good investment
Solution b
1) Investment type- Perpetuity
Rate of return- 8%
Cash flows= $700 from t3
PV= 700
r ∗(1+r )−3
Steps on Calculator
Input equation directly as above and solve
=$6,946.03
2) Investment type- Uneven cash flow
Rate of return- 8%
t1=500, t2=1000, t3=1500, t4=2000 t5=2500 t6=3000
PV=500*(1+r )−1+1000*(1+r )−2+1500*(1+r )−3+2000*(1+r )−4+2500*(1+r )−5+3000*
(1+r )−6

Steps on Calculator
o Input the cash flows for (1,2.3,4,5 & 6) using CF and N
o Input 8% and press I/YR
o Press the NPV key to solve
= $7,573.08
Conclusion- I will chose the uneven cash flow investment since it has a greater present
value than the perpetuity investment
Question 3 Solutions
Part a
Future Value= $50,000
Interest rate= 6% p.a compounded monthly
I= 0.06/12= 0.5%=0.005
Monthly payment (PMT)= X
T= 60
50,000= X*¿ ¿
Steps on Calculator
o Input 50,000 and press FV
o Input 60 and press N
o Input 0.5% and press I/YR
o Input 0 and press PV
o Press the PMT key to solve for the payment
PMT= $716.64

Part b
We need to compare the following cash flows
 Future Value of ETF Fund at Retirement age, i.e. t=35
 Present Value of the retirement monthly payments (annuity) at Retirement age,
i.e. t=35
If PV of annuity at retirement > FV of ETF fund value at retirement age, then it will not
be able to support the allowance.
FV of ETF fund at Retirement Age @9.3807% pa
(Note 9% p.a compounded monthly has effective rate of 9.3807%-)
= 50,000* (1+9.3807 % )30
Steps on calculator
o To determine effective interest rate, enter nominal rate 9 press Nom %
o Enter compounding period 12, press P/YR
o Press shift ,EFF% to solve effective interest rate- you get 9.3807%
o Store Interest rate
o Next Input directly 50,000*(1+ I /YR)30 and solve
=$736,528.81
5 6035
0
t=0 30
ETF @9% p.a compounded
monthly
Monthly Income @6% p.a comp monthly

PV of annuity at Retirement age
Assumption- No inflation, therefore interest rate is 6% p.a compounded monthly
=6000*( 1−( 1+ 0.06
12 )
−300
0.06/12
)
Steps on Calculator
o Input 6,000 and press PMT
o Input 300 and press N
o Input 0.5% and press I/YR
o Press the PV key to solve
=$931,241
Since $931,241 > 736,529, the ETF investment will not be enough to support the
monthly retirement income.

Question 4 Solutions
Part a
Interest= 8.3 % p.a
Monthly Period interest rate= (1+8.3%)^(1/12) -1= 0.6667%
Monthly Pmt= $3,000
t=36
PV= 3,000*( 1− ( 1+0.00667 )−36
0.00667 )
Steps on Calculator
 Input 3,000 and press PMT
 Input 36 and press N
 Input 0.667% and press I/YR
 Press the PV key to solve
=$95,735.35
Part b
Comparison Nominal to Effective
Nominal interest is a rate used for describing a loan or investment interest. It has no
consideration to compounding. It can be stated for any time period: Annually,
semiannually, quarterly, monthly, weekly, daily, etc.
On the other hand, Effective Interest Rate takes into consideration compounding and
reflects the true scenario making it more useful than the nominal.
Comparison compounding period to Effective
Compounding period interest rate and effective Interest rate both take compounding into
consideration. However, periodic interest rate is stated on the basis of compounding
period e.g. per month, per quarter. The effective rate is stated on an annual basis.

It is important to note that when doing computations, one can find that the frequency of
interest compounding is not the same as the frequency of cash flows. Therefore, it is
important to ensure that the payment period and compounding period are on the same
basis, and that the interest rate and the number of periods are adjusted as well.