A. 2017
1. (a)
Buy now (- cost now) Yes (at prob = 1 - non use prob) FV
No 0
< Wait (0) Yes ( at prob cal. above) + FV
- cost later
No 0
Effective rate = [(1+ cost of capital)^(months/12)] – 1
Net expected value (buy now)= (1- probability not use) x FV x 1/ [(1+cost of
capital)^(months/12)] – cost now
Net expected value (buy later) = (1-probability not use)x(FV-cost later) x 1/[(1+cost
of capital)^(months/12)]
-> best to do now or later?
(b)
Relevance costs Irrelevant costs
Income from sales Market research (already spent so not
Cost of sales affected whether or not we decide to
Cost of new staff pursue the project)
Depreciation – not itself relevant but is an allowable expense against tax so we
have to include it to the extent that it influences our calculation of tax to be paid
NPV analysis
Sales (units) (provided) Yr1unit x (1+%) Yr2unit x (1+%)
Year 0 1 2 3
-Initial investment (prov.)
+Sales income = units x price per unit
-Cost of sales = Sales income x %
-New staff cost (prov.)
-Marketing campaign (prov.) (to be included in the year stated)
-Depreciation Straightline = initial investment / years
Taxable profit X X X
-Tax = taxable profit x %
Profit after tax Y Y Y
+Depreciation (calculated above)
Cash flow from Z Z Z Z
project after tax
Present value factor = 1/[(1+%requiredreturn)^(yr 0 or yr 1 or yr2 or yr3)
Present value (GBP) Cash flow from project after tax x present value factor
NPV = total of present values
-> negative – do not take, positive – take
(c) Black-Scholes approach: second project
t = years for 2nd project to commence since project 1 starts
X = initial investment for second project
o= volatility
r= risk-free rate of interest pa
, p= ln(1+r) (TAKE 5 DECIMAL FIGURES)
So= PV of the 2nd project expected after-tax operating CF (=CF * (1-attribute))
C S 0 N d 1 X e t N d 2 Use ROUNDED d1 and d2
calculated to find A and B in
ln S 0 X 0.5 2 t NorDistribution Table
d1 N(d1) = A (if negative or close to
t
68-95-99.7 -> N = 1-A)
ln S 0 X 0.5 2 t
d2 d 1 t N(d2) = B (if negative or close to
t
68-95-99.7 -> N= 1-B)
If project 2 is available, do not invest now; rather, wait. Then, expected value of project 2 as
a call option via Black-Scholes is ___ (just cal.). So maximum wealth loss tolerable from
project 1 is ___ (just cal.)
( if calculated NPV before Black-Scholes -> At expected valuation, the follow-on option still
does not make the first project worthwhile – but the values are small and close. The overall
NPV could change if forecasts are slightly wrong, rates change, etc. Probably better to try to
find another project with a higher profitability index)
2. (b) M&M framework – no tax
Same level of risk, same net income (remain constant)
A plc: equity + debt
B plc: equity only
Shareholder owning X% equity at A plc -> increase income how?
This is within the M&M framework. The firms have the same business risk, the same NOI, and there
is no corporation tax - therefore, per M&M1, the firms should have same value. The existence of
debt (and, therefore, financial risk) in A plc’s capital structure should be reflected by a cost of equity
in for A plc which is sufficiently greater than that of B plc to ensure that A plc's WACC is equal to B
plc's cost of equity.
But the firms’ WACCs are obviously not equal, since we see a value difference (total Aplc value
versus total Bplc value).
To achieve the M&M value equilibrium, the value of A plc must fall relative to the value of B plc; or,
equivalently, the value of B plc must rise relative to the value of A plc. In market/trading adjustment
terms, this price adjustment would arise if shareholders of A plc sold their shares and reinvested the
proceeds in B plc. Shareholders would only have an incentive to do this if it gave rise to a profit,
assuming all else (including risk) is unaffected. To maintain the level of financial risk borne by the
shareholder and therefore make the returns comparable, it is necessary for the individual to borrow
a certain amount, i.e. substituting home-made leverage for corporate leverage. The amount to be
borrowed is determined by the debt equity ratio of A plc, which is 1:1. For the shareholder with an
investment of X% equity of A plc:
%debt = % debt prov. * nominal value/ market value
Proceeds from sale of shares in A plc = A plc equity x %
Cash borrowed = above x debt equity ratio at A plc
sum = total proceeds available to re-invest
1. (a)
Buy now (- cost now) Yes (at prob = 1 - non use prob) FV
No 0
< Wait (0) Yes ( at prob cal. above) + FV
- cost later
No 0
Effective rate = [(1+ cost of capital)^(months/12)] – 1
Net expected value (buy now)= (1- probability not use) x FV x 1/ [(1+cost of
capital)^(months/12)] – cost now
Net expected value (buy later) = (1-probability not use)x(FV-cost later) x 1/[(1+cost
of capital)^(months/12)]
-> best to do now or later?
(b)
Relevance costs Irrelevant costs
Income from sales Market research (already spent so not
Cost of sales affected whether or not we decide to
Cost of new staff pursue the project)
Depreciation – not itself relevant but is an allowable expense against tax so we
have to include it to the extent that it influences our calculation of tax to be paid
NPV analysis
Sales (units) (provided) Yr1unit x (1+%) Yr2unit x (1+%)
Year 0 1 2 3
-Initial investment (prov.)
+Sales income = units x price per unit
-Cost of sales = Sales income x %
-New staff cost (prov.)
-Marketing campaign (prov.) (to be included in the year stated)
-Depreciation Straightline = initial investment / years
Taxable profit X X X
-Tax = taxable profit x %
Profit after tax Y Y Y
+Depreciation (calculated above)
Cash flow from Z Z Z Z
project after tax
Present value factor = 1/[(1+%requiredreturn)^(yr 0 or yr 1 or yr2 or yr3)
Present value (GBP) Cash flow from project after tax x present value factor
NPV = total of present values
-> negative – do not take, positive – take
(c) Black-Scholes approach: second project
t = years for 2nd project to commence since project 1 starts
X = initial investment for second project
o= volatility
r= risk-free rate of interest pa
, p= ln(1+r) (TAKE 5 DECIMAL FIGURES)
So= PV of the 2nd project expected after-tax operating CF (=CF * (1-attribute))
C S 0 N d 1 X e t N d 2 Use ROUNDED d1 and d2
calculated to find A and B in
ln S 0 X 0.5 2 t NorDistribution Table
d1 N(d1) = A (if negative or close to
t
68-95-99.7 -> N = 1-A)
ln S 0 X 0.5 2 t
d2 d 1 t N(d2) = B (if negative or close to
t
68-95-99.7 -> N= 1-B)
If project 2 is available, do not invest now; rather, wait. Then, expected value of project 2 as
a call option via Black-Scholes is ___ (just cal.). So maximum wealth loss tolerable from
project 1 is ___ (just cal.)
( if calculated NPV before Black-Scholes -> At expected valuation, the follow-on option still
does not make the first project worthwhile – but the values are small and close. The overall
NPV could change if forecasts are slightly wrong, rates change, etc. Probably better to try to
find another project with a higher profitability index)
2. (b) M&M framework – no tax
Same level of risk, same net income (remain constant)
A plc: equity + debt
B plc: equity only
Shareholder owning X% equity at A plc -> increase income how?
This is within the M&M framework. The firms have the same business risk, the same NOI, and there
is no corporation tax - therefore, per M&M1, the firms should have same value. The existence of
debt (and, therefore, financial risk) in A plc’s capital structure should be reflected by a cost of equity
in for A plc which is sufficiently greater than that of B plc to ensure that A plc's WACC is equal to B
plc's cost of equity.
But the firms’ WACCs are obviously not equal, since we see a value difference (total Aplc value
versus total Bplc value).
To achieve the M&M value equilibrium, the value of A plc must fall relative to the value of B plc; or,
equivalently, the value of B plc must rise relative to the value of A plc. In market/trading adjustment
terms, this price adjustment would arise if shareholders of A plc sold their shares and reinvested the
proceeds in B plc. Shareholders would only have an incentive to do this if it gave rise to a profit,
assuming all else (including risk) is unaffected. To maintain the level of financial risk borne by the
shareholder and therefore make the returns comparable, it is necessary for the individual to borrow
a certain amount, i.e. substituting home-made leverage for corporate leverage. The amount to be
borrowed is determined by the debt equity ratio of A plc, which is 1:1. For the shareholder with an
investment of X% equity of A plc:
%debt = % debt prov. * nominal value/ market value
Proceeds from sale of shares in A plc = A plc equity x %
Cash borrowed = above x debt equity ratio at A plc
sum = total proceeds available to re-invest
