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VIPSolutions · Accepted Answer

# Objective

Calculate the change in monthly profit (on a present value basis) for Microbiotics when credit is offered to customers, using the provided data and specified interest rates.

---

## Given Data

- **Price per carton (P):** $130  
- **Cost per carton (C):** $80  
- **Current sales:** 1,080 cartons/month  
- **Expected sales if credit is granted:** 1,140 cartons/month  
- **Increase in sales:** 1,140 - 1,080 = 60 cartons/month  
- **Credit period:** 1 month  
- **Interest rate (r):** (varies by part)  
- **All customers pay on time and take full credit period**

---

## Step 1: Calculate Additional Monthly Profit (Before Discounting)

$$
\text{Incremental Profit (before discounting)} = \text{Increase in sales} \times (\text{Price per carton} - \text{Cost per carton})
$$

$$
\text{Incremental Profit} = 60 \times (130 - 80)
$$
$$
\text{Incremental Profit} = 60 \times 50 = \$3,000
$$

---

## Step 2: Calculate Present Value of Sales Receipts

Since customers pay in one month, receipts are discounted by 1 month at the interest rate.

$$
\text{PV} = \frac{\text{Incremental Profit}}{(1 + r)}
$$

---

## (a) Interest rate = 1% per month

$$
r = .01
$$

$$
\text{PV} = \frac{3,000}{1 + .01}
$$
$$
\text{PV} = \frac{3,000}{1.01}
$$
$$
\text{PV} = 2,970.30
$$

### **Change in total monthly profit = \$2,970.30**

---

## (b) Interest rate = 1.5% per month

$$
r = .015
$$

$$
\text{PV} = \frac{3,000}{1 + .015}
$$
$$
\text{PV} = \frac{3,000}{1.015}
$$
$$
\text{PV} = 2,958.13
$$

### **Change in total monthly profit = \$2,958.13**

---

## (c) Credit offered only to new customers (interest rate = 1.5% per month)

- Only the additional 60 cartons are sold on credit; the original 1,080 cartons remain cash sales.
- Only incremental profit (from 60 cartons) is discounted.

$$
\text{Incremental Profit from new customers} = 60 \times (130 - 80) = \$3,000
$$
$$
\text{PV (new customers only)} = \frac{3,000}{1.015}
$$
$$
\text{PV} = 2,958.13
$$

**Since there is no change for the original customers, the change in total monthly profit is only from new customers.**

### **Change in total monthly profit = \$2,958.13**

---

# Final Answers

### (a) Change in total monthly profit = **\$2,970.30**
### (b) Change in total monthly profit = **\$2,958.13**
### (c) Change in total monthly profit = **\$2,958.13**

---

**Crux:**  
The increase in profit is slightly lower when accounting for the time value of money at higher interest rates, but since all new sales are due to offering credit, the profit increase is the present value of incremental profit from increased sales.

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