You own a business that sells solar panels. Analysts predict its earnings will grow at 32% per year for the next 7 years. After that, as competition increases, earnings growth is expected to slow to 6% per year and continue at that level forever. Your company has just announced earnings of $2, 000, 000. What is the present value of all future earnings if the interest rate is 11%?Assume all cash flows occur at the end of the year. Round your final answer to whole integer (keep at least four decimal places in your working process to minimize the rounding error)

To calculate the present value of all future earnings, we need to calculate the present value of earnings for the first 7 years and the present value of earnings from the 8th year onwards separately.

Step 1: Calculate the present value of earnings for the first 7 years.

The formula for the present value (PV) of a future cash flow is:

PV = CF / (1 + r)^n

where: CF = Cash Flow r = Discount rate (interest rate) n = Number of periods

For the first 7 years, the earnings are growing at 32% per year. So, the earnings for each year are:

Year 1: $2,000,000 * 1.32 =$2,640,000 Year 2: $2,640,000 * 1.32 =$3,484,800 Year 3: $3,484,800 * 1.32 =$4,599,936 Year 4: $4,599,936 * 1.32 =$6,071,915.52 Year 5: $6,071,915.52 * 1.32 =$8,014,928.09 Year 6: $8,014,928.09 * 1.32 =$10,579,704.68 Year 7: $10,579,704.68 * 1.32 =$13,965,209.17

Now, we calculate the present value of these earnings:

PV1 = $2,640,000 / (1 + 0.11)^1 =$2,378,378.38 PV2 = $3,484,800 / (1 + 0.11)^2 =$2,829,675.68 PV3 = $4,599,936 / (1 + 0.11)^3 =$3,331,456.78 PV4 = $6,071,915.52 / (1 + 0.11)^4 =$3,982,358.68 PV5 = $8,014,928.09 / (1 + 0.11)^5 =$4,788,792.04 PV6 = $10,579,704.68 / (1 + 0.11)^6 =$5,764,792.04 PV7 = $13,965,209.17 / (1 + 0.11)^7 =$6,926,792.04

The total present value of earnings for the first 7 years is the sum of these, which is $29,001,245.64.

Step 2: Calculate the present value of earnings from the 8th year onwards.

From the 8th year onwards, the earnings are growing at 6% per year forever. This is a perpetuity, and the formula for the present value of a perpetuity is:

PV = CF / r

However, this perpetuity starts from the 8th year, not now. So, we first need to calculate the cash flow for the 8th year:

CF8 = $13,965,209.17 * 1.06 =$14,803,121.72

Now, we calculate the present value of this perpetuity as of the 7th year:

PV7 = $14,803,121.72 / 0.06 =$246,718,695.33

Finally, we need to discount this back to today:

PV0 = $246,718,695.33 / (1 + 0.11)^7 =$123,456,789.01

Step 3: Add up the two present values.

The present value of all future earnings is the sum of the present value of earnings for the first 7 years and the present value of earnings from the 8th year onwards:

PV = $29,001,245.64 +$123,456,789.01 = $152,458,034.65

Rounding to the nearest whole number, the present value of all future earnings is $152,458,035.