Part I. Master Budgets

Farmer Manufacturing, Inc. prepares their budgets on a quarterly basis. Below is information which will be used to prepare their first quarter budget.

Forecasted sales in units for each product are as follows:

The average selling price is $36 per unit.

Below is additional information which will be needed to prepare the master budget:

Company policy requires that each month’s ending inventory (finished goods) be equal to 40% of the next month’s estimated sales. Ending inventory on December 31 was 8,800 units. Sales for April are projected to be 39,000 units, and sales for May are projected to be 42,000 units.

Information on material and labor requirements include:

Company policy requires that the ending inventory for raw material be equal to 30% of the following month’s estimated material requirements. Ending inventory on December 31 for Ingredient Q was 20,800 pounds.

Manufacturing overhead includes both variable and fixed components. Overhead is allocated based on direct labor hours. Variable overhead is budgeted at $3.25 per direct labor hour required. Fixed overhead is budgeted at $34,500 per month.

Selling expenses include sales commissions and sales salaries. Commissions are paid at 4% of sales. Monthly sales salaries are $4,200. General and administrative expenses are $6,400 per month.

Part I Requirements:

1. Prepare a monthly Sales Budget for the first quarter.
2. Prepare a monthly Production Budget for the first quarter.
3. Prepare a monthly Direct Material Purchases Budget for the first quarter.
4. Prepare a monthly Direct Labor Budget for the first quarter.
5. Prepare a monthly Overhead Budget for the first quarter.
6. Prepare a monthly Selling, General, & Administrative Expense Budget for the first quarter.

Problem 2.1 Calculate the present value of $10,000 due in 7 months using 6% p.a. simple interest.

Problem 2.2 A note with a maturity value of $100,000 was purchased 46 days before maturity for $99,218.63. Calculate the rate of simple interest p.a. used.

Problem 2.3 Calculate the present (discounted) value at 5% p.a. payable monthly of $1,000.

(a) due at the end 4 years,

(b) due at the end 6 years.

Problem 2.4 If j₄ = 5:8% calculate

(a) j₂,

(b) j₁₂.

Problem 2.5 A person has debts of $1,000 due on 1 July 2013 and $2,000 due on 1 January 2015. He wishes to pay $500 on 1 January 2014 and $X on 1 January 2016. Calculate X if interest is at 7% p.a. convertible half-yearly.

Problem 2.6 How long will it take for $2,000 to accumulate to $3,000 at 6%p.a. compounded continuously?

Problem 2.7 Investor A contributes $2,000 annually into a fund, the first deposit being on his 26th birthday and the last on his 65th birthday. How much will be in the fund immediately after the final deposit? Interest is at j₁ = 8%.

Problem 2.8 A company wishes to accumulate $100,000 by the end of 5 years. What level deposit should be made at the end of each quarter for 5 years if interest is at j₄ = 8%?

Problem 2.9 $500 is deposited at the end of each half-year for 10 years. Calculate the amount at the end of 10 years if interest is at j₂ = 5% for 3 years and j₂ = 7% thereafter.

Problem 2.10 Instead of paying $100 at the beginning of each month for 1 year, a person wants to make a single payment at the beginning of the year. Using j₁₂ = 6% how much should be paid at the beginning of the year?

Problem 2.11 A bond with face value of $100 and interest at j₂ = 7% is to be redeemed at par in 6 years.

(a) What is the size of the half-yearly interest payments?

(b) What is the size of the redemption payment?

(c) Draw a timeline showing the price paid (P), the interest payments and the redemption

payment.

(d) From your timeline, write down an equation of value, and hence calculate the price if

the yield to maturity is j₂ = 8%.

Write a program to validate parenthesis of any given equation by using the following criteria (you MUST use stacks); Number of open parenthesis “(“must be same as number of close parentheses “)” For example if I input “3 + 4 * (98+34*(34+8)*34*(3+x)” the program should display an error message, because number of open parenthesis “(“is 3 and number of closed “)” parenthesis is 2.

Stack-Driver.cpp:

#include "stack.h"
#include "stack.cpp"
#include<stdio.h>
#include<stdlib.h>
#include<time.h>

int main() {
   stack<int> my_stack(100);
   srand(time(NULL));
   for (int i = 0; i < 10; i++) {
       my_stack.push(rand() % 10 + 1);
   }
   cout << "stack size is: " << my_stack.getSize() << endl;
   cout << "top of the stack: " << my_stack.peek() << endl;
   while (!my_stack.isEmpty())
       cout << my_stack.pop() << " - ";
   cout << endl;
   //my_stack.~stack();

}

Stack.h:

#pragma once
#ifndef STACK_H
#define STACK_H
#include<iostream>
using namespace std;
template<class T>
class stack
{
public:
   stack(int ); // constructor
   ~stack();
   T peek(); // returns the top item from stack without removing
   void push(T anItem);
   T pop(); // remove top element and return it
   bool isEmpty(); // check if teh stack is empty
   //void print_the_stack();
   int getSize(); // return size of stack
private:
   T* a;
   int size;// count howmany items are in the stack
   int capacity;// maximum capacity of the stack

};
#endif // !STACK_H

Stack.cpp:

#include "stack.h"
template<class T>
stack<T>::stack(int capacity) {

   size = 0;
   this->capacity = capacity;
   a = new T[capacity];
}
template<class T>
T stack<T>::peek() {
   return a[size-1];
}

template<class T>
void stack<T>::push(T anItem) {
   a[size] = anItem;
   size++;
}
template<class T>
T stack<T>::pop() {
   if (size >0) {
       size--;
       return a[size];
   }
}

template<class T>
int stack<T>::getSize() {
   return size;
}
template<class T>
bool stack<T>::isEmpty() {
   return size > 0 ? false : true;
}
template<class T>
stack<T>::~stack() {
   delete[] a;
}

A perfectly competitive market operates in a market with an equilibrium price of P. Its total cost is given by TC = FC + VC(q), where FC (>0) is the fixed cost, VC(q) is the variable cost and and q is the quantity produced by the firm.

1. Write down the optimization problem of this firm.

2. Write down the first order condition. (Assume from now on the equation formed by the first order condition has an interior solution q*>0.)

3. Write down the second order condition(s). What does it say about the shape of the function VC(q).

4. Use the first order condition with the implicit function theorem to calculate ?q*/?FC. Prove that the supply function of this perfectly competitive firm is upward sloping.

The manufacturer of an MP3 player wanted to know whether a 10% reduction in price is enough to increase the sales of its product. To investigate, the owner randomly selected eight outlets and sold the MP3 player at the reduced price. At seven randomly selected outlets, the MP3 player was sold at the regular price. Reported below is the number of units sold last month at the regular and reduced prices at the randomly selected outlets.

Regular price 138 121 123 116 116 122 132 Reduced price 143 133 151 136 144 123 130 131 picture Click here for the Excel Data File At the 0.01 significance level, can the manufacturer conclude that the price reduction resulted in an increase in sales? Hint: For the calculations, assume reduced price as the first sample.

Compute the pooled estimate of the variance. (Round your answer to 3 decimal places.)

Compute the test statistic. (Round your answer to 2 decimal places.)

State your decision about the null hypothesis. Reject H0 Fail to reject H0

he manufacturer of an MP3 player wanted to know whether a 10% reduction in price is enough to increase the sales of its product. To investigate, the owner randomly selected eight outlets and sold the MP3 player at the reduced price. At seven randomly selected outlets, the MP3 player was sold at the regular price. Reported below is the number of units sold last month at the regular and reduced prices at the randomly selected outlets.

  Click here for the Excel Data File

At the 0.010 significance level, can the manufacturer conclude that the price reduction resulted in an increase in sales? Hint: For the calculations, assume reduced price as the first sample.

1. Compute the pooled estimate of the variance. (Round your answer to 3 decimal places.)

2. Compute the test statistic. (Round your answer to 2 decimal places.)

3. State your decision about the null hypothesis.

• Fail to reject H₀

• Reject H₀

Amazon is a monopolist in the textbook market. Amazon is currently selling textbooks only in the US. The demand for textbook is given by: P = 210 − Q.

The marginal cost of producing textbook is MC = 5. there is no fixed cost.

1. (a) Compute the profit-maximizing price and quantity.

2. (b) Compute the deadweight loss due to monopoly power.

3. (c) If Amazon can use first-degree price discrimination, what is its profit? Is there any deadweight loss?

4. (d) Suppose that Amazon is deciding whether to also sell textbooks in Wakanda. The demand for textbook in Wakanda is given by: P = 70 − Q

   1. (i) If Amazon can price discriminate between US and Wakanda, what are the optimal prices

      and quantities?

   2. (ii) If Amazon cannot price discriminate between US and Wakanda, what are the optimal price and quantities?

   3. (iii) Using your answers in (i) and (ii), which country is better off with price discrimination? Which country is worse off?

   4. (iv) How would your answer to (i) change if the cost function is given by TC(Q) = 0.5Q2?

5. (e) Give an example of second-degree price discrimination.

Assume that you are the V.P. of marketing for a company (manufacturer) that produces refrigerated prepared pasta dishes for sale to consumers through various retail channels. You are considering producing a new line of all natural one-serving pasta dishes.

This is a new product that will appeal to health-conscious consumers.

Top management is committed to invest $400,000 in equipment to start production. You ordered and paid $3,000 to a specialized marketing research company to assess a value that potential buyers will see in your product and their willingness to pay. Research findings suggest that consumers would only be willing to buy the pasta if the price is less than $6.00 per package.

You will be selling the pasta through specialty food brokers who will distribute to natural food stores who will sell to consumers. The natural food stores require a 30 percent retailer margin and the brokers require a 20 percent wholesaler margin. Treat retailer and wholesaler margins as markups on price (not as markups on cost).

In addition, you plan to run promotional campaign to introduce your product to

potential buyers. This will cost you $12,000 during the first four months. You do not plan to spend any money on promotion after the first four months as all potential buyers by that time will be aware of your product.

1. Assuming the natural food stores will sell the product for $5.99 per package, what price will the specialty food brokers charge the food stores for the product?
2. What price will the manufacturer charge the specialty food brokers?
3. If the manufacturer costs are $0.95 per package, what will the manufacturer’s contribution per unit be (or fixed cost contribution)?
4. How many all natural one-serving pasta dishes the manufacturer needs to sell during the first year to break even?

Question (Double Marginalization)

Suppose that Michelin is the only producer of tires and Toyota the only producer of cars. The demand function for cars is given by Q = 40 − 4P. Michelin's (constant) cost of production for a set of five tires is 3. The production of one car requires a set of five tires and a bundle of inputs, which Toyota can obtain at a price of 6.
- Suppose first that Michelin and Toyota are just two departments within the same firm.

1. (a) What price would the firm charge for cars and how many cars would it produce?

- Suppose now that Michelin and Toyota are separate firms. Michelin quotes a price w for a set of five tires and Toyota decides how many sets to buy at that price.

2. (b) What price will Michelin set? How many cars will Toyota sell and at what price?

3. (c) Are consumers better off when Michelin and Toyota are an integrated firm [Part (a)] or when they are separate firms [Part (b)]?