Question

Ch 30 Q1.

The Branding Iron Company sells its irons for $56 apiece wholesale. Production cost is $46 per iron. There is a 31% chance that wholesaler Q will go bankrupt within the next year. Q orders 1,000 irons and asks for seven months’ credit. Assume that the discount rate is 11% per year, there is no chance of a repeat order, and Q will pay either in full or not at all.

a. Calculate the NPV of the order. (A negative answer should be indicated by minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places.)

NPV            $ ___________

b. Should you accept the order?

	Yes
	No

Answer 1

Solution:

a.Calculation of NPV of the order:

As per the information given in the question we have

Price per piece of Iron = $ 56 ; Production cost per piece of Iron = $ 46 ; No. of Iron pieces per order = 1,000 ;

The total production cost / cash outflows = Production cost per piece of Iron * No. of Iron pieces per order

= $ 46 * 1,000 = $ 46,000

The total sales revenue / cash inflows from the order = Price per piece of Iron * No. of Iron pieces per order

= $ 56 * 1,000 = $ 56,000

Total sales revenue / cash inflows from the order = $ 56,000

Further as per the information given in the question we have

There is a 31% chance that wholesaler Q will go bankrupt within the next year and the total sales revenue may not be received.

Thus the realisable sales revenue = Total sales revenue * ( 1 – Probability of going bankrupt )

= $ 56,000 * ( 1 – 0.31 ) = $ 56,000 * 0.69

= $ 38,640

Thus the realisable sales revenue / cash inflows = $ 38,640

Calculation of the present value of realisable cash inflows from the order :

The present value of a cash inflow at period 'n' is calculated using the following formula:

PV = C / (1 + r )n

PV = Present Value   ; C : Cash inflow at period n ; r = discount rate ; n = Number of years

As per the information given in the question we have

r = 11 % = 0.11 ; C = $ 38,640 ; n = 7 months = ( 7/ 12 ) years= 0.583333 years ; ( since credit is issued for a period of seven months )

Applying the above values in the formula we have

= $ 38,640 / ( 1 + 0.11 ) 0.583333

= $ 38,640 / ( 1.11 ) 0.583333

= $ 38,640 / 1.062768

= $ 36,357.893524

The formula for calculating the NPV of the order is = Present value of cash Inflow – Initial cash outflow

As per the information available we have

Present value of cash Inflow = $ 36,357.893524   ; Initial cash outflow = Total Production cost = $ 46,000

Thus the NPV of the order is = $ 36,357.893524 - $ 46,000

= - $ 9,642.106476

= - $ 9,642.11 ( when rounded off to two decimal places )

Thus the NPV of the order is = - $ 9,642.11

b.Since the NPV of the order is negative, the order should not be accepted.

The solution is No.

Note : The value of ( 1.11 ) 0.583333   has been calculated using the excel function =POWER(Number,Power). Thus =POWER(1.11,0.583333) = 1.062768